{"id":287,"date":"2021-11-06T20:53:35","date_gmt":"2021-11-06T12:53:35","guid":{"rendered":"https:\/\/www.lazybirds.top\/?p=287"},"modified":"2022-01-03T10:34:22","modified_gmt":"2022-01-03T02:34:22","slug":"%e6%a6%82%e7%8e%87%e8%ae%ba-%e6%9c%9f%e4%b8%ad%e5%a4%8d%e4%b9%a0","status":"publish","type":"post","link":"https:\/\/www.lazybirds.top\/?p=287","title":{"rendered":"\u6982\u7387\u8bba &#8211; \u671f\u4e2d\u590d\u4e60"},"content":{"rendered":"\n<p>\u7b2c\u4e00\u81f3\u56db\u7ae0<\/p>\n\n\n\n<!--more-->\n\n\n\n      <meta charset=\"utf-8\">\n      <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n      \n      <link rel=\"stylesheet\" href=\"https:\/\/www.lazybirds.top\/katex\/katex.min.css\">\n      \n      \n      \n      \n      \n      \n      \n      \n      \n      <style>\n      \/**\n * prism.js Github theme based on GitHub's theme.\n * @author Sam Clarke\n *\/\ncode[class*=\"language-\"],\npre[class*=\"language-\"] {\n  color: #333;\n  background: 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class=\"vlist-r\"><span class=\"vlist\" style=\"height:2.6500000000000004em;\"><span style=\"top:-4.8100000000000005em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.05017em;\">B<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.05017em;\">B<\/span><span class=\"mclose\">)<\/span><\/span><\/span><span style=\"top:-3.61em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07153em;\">BC<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.05017em;\">B<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07153em;\">C<\/span><span class=\"mclose\">)<\/span><\/span><\/span><span style=\"top:-2.4099999999999997em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07153em;\">C<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07153em;\">C<\/span><span class=\"mclose\">)<\/span><\/span><\/span><span style=\"top:-1.2099999999999997em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07153em;\">BC<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.05017em;\">B<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07153em;\">C<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:2.1500000000000004em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width:0.5em;\"><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>&#x5219;&#x79F0;A&#x3001;B&#x3001;C&#x662F;&#x76F8;&#x4E92;&#x72EC;&#x7ACB;&#x7684;&#x968F;&#x673A;&#x4E8B;&#x4EF6;<\/p>\n<p>&#x6CE8;&#x610F;&#xFF1A;<br>\n&#x5728;&#x4E09;&#x4E2A;&#x4E8B;&#x4EF6;&#x72EC;&#x7ACB;&#x6027;&#x7684;&#x5B9A;&#x4E49;&#x4E2D;&#xFF0C;&#x56DB;&#x4E2A;&#x7B49;&#x5F0F;&#x662F;&#x7F3A;&#x4E00;&#x4E0D;&#x53EF;&#x7684;&#xFF0E;&#x5373;&#xFF1A;&#x524D;&#x4E09;&#x4E2A;&#x7B49;&#x5F0F;&#x7684;&#x6210;&#x7ACB;&#x4E0D;&#x80FD;&#x63A8;&#x51FA;&#x7B2C;&#x56DB;&#x4E2A;&#x7B49;&#x5F0F;&#x7684;&#x6210;&#x7ACB;&#xFF1B;&#x53CD;&#x4E4B;&#xFF0C;&#x6700;&#x540E;&#x4E00;&#x4E2A;&#x7B49;&#x5F0F;&#x7684;&#x6210;&#x7ACB;&#x4E5F;&#x63A8;&#x4E0D;&#x51FA;&#x524D;&#x4E09;&#x4E2A;&#x7B49;&#x5F0F;&#x7684;&#x6210;&#x7ACB;&#xFF0E;<\/p>\n<h3 class=\"mume-header\" id=\"%E7%8B%AC%E7%AB%8B%E6%80%A7%E6%8E%A8%E5%B9%BFn%E4%BA%8B%E4%BB%B6\">&#x72EC;&#x7ACB;&#x6027;&#x63A8;&#x5E7F;&#x2014;&#x2014;n&#x4E8B;&#x4EF6;<\/h3>\n\n<p>&#x8BBE;A1,A2,&#x2026;,A&#x1D45B;&#x662F;n&#x4E2A;&#x968F;&#x673A;&#x4E8B;&#x4EF6;&#xFF0C;&#x5982;&#x679C;&#x6EE1;&#x8DB3;<br>\n<span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo fence=\"true\">{<\/mo><mtable rowspacing=\"0.1600em\" columnalign=\"center center\" columnspacing=\"1em\"><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mrow><mi mathvariant=\"normal\">P<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi mathvariant=\"normal\">A<\/mi><mi>i<\/mi><\/msub><msub><mrow><mtext>&#xA0;<\/mtext><mi mathvariant=\"normal\">A<\/mi><\/mrow><mi mathvariant=\"normal\">j<\/mi><\/msub><mo fence=\"true\">)<\/mo><\/mrow><mo>=<\/mo><mi mathvariant=\"normal\">P<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi mathvariant=\"normal\">A<\/mi><mi>i<\/mi><\/msub><mo fence=\"true\">)<\/mo><\/mrow><mi mathvariant=\"normal\">P<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi mathvariant=\"normal\">A<\/mi><mi>j<\/mi><\/msub><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mrow><mo stretchy=\"false\">(<\/mo><mn>1<\/mn><mo>&#x2264;<\/mo><mi>i<\/mi><mo>&lt;<\/mo><mi>j<\/mi><mo>&#x2264;<\/mo><mi>n<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mrow><mi mathvariant=\"normal\">P<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi mathvariant=\"normal\">A<\/mi><mi>i<\/mi><\/msub><msub><mrow><mtext>&#xA0;<\/mtext><mi mathvariant=\"normal\">A<\/mi><\/mrow><mi mathvariant=\"normal\">j<\/mi><\/msub><msub><mi mathvariant=\"normal\">A<\/mi><mi>k<\/mi><\/msub><mo fence=\"true\">)<\/mo><\/mrow><mo>=<\/mo><mi mathvariant=\"normal\">P<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi mathvariant=\"normal\">A<\/mi><mi>i<\/mi><\/msub><mo fence=\"true\">)<\/mo><\/mrow><mi mathvariant=\"normal\">P<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi mathvariant=\"normal\">A<\/mi><mi>j<\/mi><\/msub><mo fence=\"true\">)<\/mo><\/mrow><mi mathvariant=\"normal\">P<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi mathvariant=\"normal\">A<\/mi><mi>k<\/mi><\/msub><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mrow><mo stretchy=\"false\">(<\/mo><mn>1<\/mn><mo>&#x2264;<\/mo><mi>i<\/mi><mo>&lt;<\/mo><mi>j<\/mi><mo>&lt;<\/mo><mi>k<\/mi><mo>&#x2264;<\/mo><mi>n<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mrow><mo>&#x2026;<\/mo><mtext>&#xA0;<\/mtext><mo>&#x2026;<\/mo><\/mrow><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mrow><mo>&#x2026;<\/mo><mtext>&#xA0;<\/mtext><mo>&#x2026;<\/mo><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mrow><mi mathvariant=\"normal\">P<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi mathvariant=\"normal\">A<\/mi><mn>1<\/mn><\/msub><msub><mrow><mtext>&#xA0;<\/mtext><mi mathvariant=\"normal\">A<\/mi><\/mrow><mn>2<\/mn><\/msub><mo>&#x2026;<\/mo><msub><mi mathvariant=\"normal\">A<\/mi><mi>n<\/mi><\/msub><mo fence=\"true\">)<\/mo><\/mrow><mo>=<\/mo><mi mathvariant=\"normal\">P<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi mathvariant=\"normal\">A<\/mi><mn>1<\/mn><\/msub><mo fence=\"true\">)<\/mo><\/mrow><mi mathvariant=\"normal\">P<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi mathvariant=\"normal\">A<\/mi><mn>2<\/mn><\/msub><mo fence=\"true\">)<\/mo><\/mrow><mo>&#x2026;<\/mo><mrow><mo fence=\"true\">(<\/mo><msub><mi mathvariant=\"normal\">A<\/mi><mi>n<\/mi><\/msub><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><\/mstyle><\/mtd><\/mtr><\/mtable><\/mrow><annotation encoding=\"application\/x-tex\">\\left\\{\\begin{array}{cc}\n\\mathrm{P}\\left(\\mathrm{A}_{i} \\mathrm{~A}_{\\mathrm{j}}\\right)=\\mathrm{P}\\left(\\mathrm{A}_{i}\\right) \\mathrm{P}\\left(\\mathrm{A}_{j}\\right) &amp; (1 \\leq i&lt;j \\leq n) \\\\\n\\mathrm{P}\\left(\\mathrm{A}_{i} \\mathrm{~A}_{\\mathrm{j}} \\mathrm{A}_{k}\\right)=\\mathrm{P}\\left(\\mathrm{A}_{i}\\right) \\mathrm{P}\\left(\\mathrm{A}_{j}\\right) \\mathrm{P}\\left(\\mathrm{A}_{k}\\right) &amp; (1 \\leq i&lt;j&lt;k \\leq n) \\\\\n\\ldots\\ \\ldots &amp; \\ldots\\ \\ldots\\\\\n\\mathrm{P}\\left(\\mathrm{A}_{1} \\mathrm{~A}_{2} \\ldots \\mathrm{A}_{n}\\right)=\\mathrm{P}\\left(\\mathrm{A}_{1}\\right) \\mathrm{P}\\left(\\mathrm{A}_{2}\\right) \\ldots\\left(\\mathrm{A}_{n}\\right)\n\\end{array}\\right.<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:4.80004em;vertical-align:-2.15002em;\"><\/span><span class=\"minner\"><span class=\"mopen\"><span class=\"delimsizing mult\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:2.65002em;\"><span style=\"top:-1.8999899999999998em;\"><span class=\"pstrut\" style=\"height:3.15em;\"><\/span><span class=\"delimsizinginner delim-size4\"><span>&#x23A9;<\/span><\/span><\/span><span style=\"top:-1.8919899999999998em;\"><span class=\"pstrut\" style=\"height:3.15em;\"><\/span><span style=\"height:0.6160000000000001em;width:0.889em;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"0.889em\" height=\"0.6160000000000001em\" style=\"width:0.889em\" viewBox=\"0 0 889 616\" preserveAspectRatio=\"xMinYMin\"><path d=\"M384 0 H504 V616 H384z M384 0 H504 V616 H384z\"\/><\/svg><\/span><\/span><span style=\"top:-3.15001em;\"><span class=\"pstrut\" style=\"height:3.15em;\"><\/span><span class=\"delimsizinginner delim-size4\"><span>&#x23A8;<\/span><\/span><\/span><span style=\"top:-4.292009999999999em;\"><span class=\"pstrut\" style=\"height:3.15em;\"><\/span><span style=\"height:0.6160000000000001em;width:0.889em;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"0.889em\" height=\"0.6160000000000001em\" style=\"width:0.889em\" viewBox=\"0 0 889 616\" preserveAspectRatio=\"xMinYMin\"><path d=\"M384 0 H504 V616 H384z M384 0 H504 V616 H384z\"\/><\/svg><\/span><\/span><span style=\"top:-4.90002em;\"><span class=\"pstrut\" style=\"height:3.15em;\"><\/span><span class=\"delimsizinginner delim-size4\"><span>&#x23A7;<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:2.15002em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"arraycolsep\" style=\"width:0.5em;\"><\/span><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:2.6500000000000004em;\"><span style=\"top:-4.8100000000000005em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathrm\">P<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathrm\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.31166399999999994em;\"><span style=\"top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mspace nobreak\">&#xA0;<\/span><span class=\"mord mathrm\">A<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.317502em;\"><span style=\"top:-2.5500000000000003em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">j<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.286108em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathrm\">P<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathrm\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.31166399999999994em;\"><span style=\"top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathrm\">P<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathrm\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.311664em;\"><span style=\"top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.05724em;\">j<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.286108em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><\/span><\/span><span style=\"top:-3.61em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathrm\">P<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathrm\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.31166399999999994em;\"><span style=\"top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mspace nobreak\">&#xA0;<\/span><span class=\"mord mathrm\">A<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.317502em;\"><span style=\"top:-2.5500000000000003em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">j<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.286108em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathrm\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.33610799999999996em;\"><span style=\"top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.03148em;\">k<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathrm\">P<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathrm\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.31166399999999994em;\"><span style=\"top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathrm\">P<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathrm\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.311664em;\"><span style=\"top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.05724em;\">j<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.286108em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathrm\">P<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathrm\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.33610799999999996em;\"><span style=\"top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.03148em;\">k<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><\/span><\/span><span style=\"top:-2.4099999999999997em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"minner\">&#x2026;<\/span><span class=\"mspace\">&#xA0;<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"minner\">&#x2026;<\/span><\/span><\/span><span style=\"top:-1.2099999999999997em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathrm\">P<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathrm\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.30110799999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mspace nobreak\">&#xA0;<\/span><span class=\"mord mathrm\">A<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.30110799999999993em;\"><span style=\"top:-2.5500000000000003em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"minner\">&#x2026;<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord\"><span class=\"mord mathrm\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.151392em;\"><span style=\"top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathrm\">P<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathrm\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.30110799999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathrm\">P<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathrm\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.30110799999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"minner\">&#x2026;<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathrm\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.151392em;\"><span style=\"top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:2.1500000000000004em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width:0.5em;\"><\/span><span class=\"arraycolsep\" style=\"width:0.5em;\"><\/span><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:2.6500000000000004em;\"><span style=\"top:-4.8100000000000005em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x2264;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\">i<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&lt;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.05724em;\">j<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x2264;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mclose\">)<\/span><\/span><\/span><span style=\"top:-3.61em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x2264;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\">i<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&lt;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.05724em;\">j<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&lt;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03148em;\">k<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x2264;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mclose\">)<\/span><\/span><\/span><span style=\"top:-2.4099999999999997em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"minner\">&#x2026;<\/span><span class=\"mspace\">&#xA0;<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"minner\">&#x2026;<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9500000000000002em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width:0.5em;\"><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><br>\n&#x5219;&#x79F0;A1,A2,&#x2026;,A&#x1D45B; &#x662F;n&#x4E2A;&#x76F8;&#x4E92;&#x72EC;&#x7ACB;&#x7684;&#x968F;&#x673A;&#x4E8B;&#x4EF6;<\/p>\n<p>&#x6CE8;&#x610F;&#x4E0A;&#x9762;&#x7B2C;i&#x884C;&#x6709;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msubsup><mi>&#x1D436;<\/mi><mi>&#x1D45B;<\/mi><mrow><mi>&#x1D456;<\/mi><mo>+<\/mo><mn>1<\/mn><\/mrow><\/msubsup><\/mrow><annotation encoding=\"application\/x-tex\">&#x1D436;_&#x1D45B;^{&#x1D456;+1}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1.071664em;vertical-align:-0.247em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.07153em;\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.824664em;\"><span style=\"top:-2.4530000000000003em;margin-left:-0.07153em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mbin mtight\">+<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.247em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#x4E2A;&#x7B49;&#x5F0F;&#xFF0C;<br>\n&#x5171;&#x6709;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msubsup><mi>C<\/mi><mi>n<\/mi><mn>2<\/mn><\/msubsup><mo>+<\/mo><msubsup><mi>C<\/mi><mi>n<\/mi><mn>3<\/mn><\/msubsup><mo>+<\/mo><mo>&#x22EF;<\/mo><mo>+<\/mo><msubsup><mi>C<\/mi><mi>n<\/mi><mi>n<\/mi><\/msubsup><mo>=<\/mo><msup><mn>2<\/mn><mi>n<\/mi><\/msup><mo>&#x2212;<\/mo><msubsup><mi>C<\/mi><mi>n<\/mi><mn>0<\/mn><\/msubsup><mo>&#x2212;<\/mo><msubsup><mi>C<\/mi><mi>n<\/mi><mn>1<\/mn><\/msubsup><mo>=<\/mo><msup><mn>2<\/mn><mi>n<\/mi><\/msup><mo>&#x2212;<\/mo><mi>n<\/mi><mo>&#x2212;<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">C_{n}^{2}+C_{n}^{3}+\\cdots+C_{n}^{n}=2^{n}-C_{n}^{0}-C_{n}^{1}=2^{n}-n-1<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1.061108em;vertical-align:-0.247em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.07153em;\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8141079999999999em;\"><span style=\"top:-2.4530000000000003em;margin-left:-0.07153em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.247em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1.061108em;vertical-align:-0.247em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.07153em;\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8141079999999999em;\"><span style=\"top:-2.4530000000000003em;margin-left:-0.07153em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">3<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.247em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.66666em;vertical-align:-0.08333em;\"><\/span><span class=\"minner\">&#x22EF;<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.93033em;vertical-align:-0.247em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.07153em;\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.664392em;\"><span style=\"top:-2.4530000000000003em;margin-left:-0.07153em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.247em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.747722em;vertical-align:-0.08333em;\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.664392em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1.061108em;vertical-align:-0.247em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.07153em;\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8141079999999999em;\"><span style=\"top:-2.4530000000000003em;margin-left:-0.07153em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.247em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1.061108em;vertical-align:-0.247em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.07153em;\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8141079999999999em;\"><span style=\"top:-2.4530000000000003em;margin-left:-0.07153em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.247em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.747722em;vertical-align:-0.08333em;\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.664392em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.66666em;vertical-align:-0.08333em;\"><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.64444em;vertical-align:0em;\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span>&#x4E2A;&#x7B49;&#x5F0F;<\/p>\n<h1 class=\"mume-header\" id=\"%E9%9A%8F%E6%9C%BA%E5%8F%98%E9%87%8F%E5%8F%8A%E5%85%B6%E5%88%86%E5%B8%83\">&#x968F;&#x673A;&#x53D8;&#x91CF;&#x53CA;&#x5176;&#x5206;&#x5E03;<\/h1>\n\n<h2 class=\"mume-header\" id=\"%E9%9A%8F%E6%9C%BA%E5%8F%98%E9%87%8F\">&#x968F;&#x673A;&#x53D8;&#x91CF;<\/h2>\n\n<p>&#x968F;&#x673A;&#x53D8;&#x91CF;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>X<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">X<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.68333em;vertical-align:0em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><\/span><\/span><\/span>&#x662F;&#x6837;&#x672C;&#x7A7A;&#x95F4;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>S<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">S<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.68333em;vertical-align:0em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.05764em;\">S<\/span><\/span><\/span><\/span>&#x4E0A;&#x7684;&#x51FD;&#x6570;<br>\n<span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>X<\/mi><mo>=<\/mo><mi>X<\/mi><mo stretchy=\"false\">(<\/mo><mi>&#x3C9;<\/mi><mo stretchy=\"false\">)<\/mo><mo separator=\"true\">,<\/mo><mo stretchy=\"false\">(<\/mo><mi>&#x3C9;<\/mi><mo>&#x2208;<\/mo><mi>S<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">X=X(\\omega),(\\omega\\in S)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.68333em;vertical-align:0em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">&#x3C9;<\/span><span class=\"mclose\">)<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">&#x3C9;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x2208;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.05764em;\">S<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/p>\n<h2 class=\"mume-header\" id=\"%E5%B8%B8%E8%A7%81%E7%A6%BB%E6%95%A3%E5%9E%8B%E9%9A%8F%E6%9C%BA%E5%8F%98%E9%87%8F%E5%88%86%E5%B8%83\">&#x5E38;&#x89C1;&#x79BB;&#x6563;&#x578B;&#x968F;&#x673A;&#x53D8;&#x91CF;&#x5206;&#x5E03;<\/h2>\n\n<h3 class=\"mume-header\" id=\"bernoulli-%E5%88%86%E5%B8%83-0-1-%E5%88%86%E5%B8%83\">Bernoulli &#x5206;&#x5E03; \/ 0-1 &#x5206;&#x5E03;<\/h3>\n\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mtable rowspacing=\"0.2500em\" columnalign=\"center\" columnspacing=\"0em\"><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mi>X<\/mi><mo>&#x223C;<\/mo><mi>B<\/mi><mo stretchy=\"false\">(<\/mo><mn>1<\/mn><mo separator=\"true\">,<\/mo><mi>p<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mi>P<\/mi><mo stretchy=\"false\">{<\/mo><mi>X<\/mi><mo>=<\/mo><mi>k<\/mi><mo stretchy=\"false\">}<\/mo><mo>=<\/mo><msup><mi>p<\/mi><mi>k<\/mi><\/msup><msup><mi>q<\/mi><mrow><mn>1<\/mn><mo>&#x2212;<\/mo><mi>k<\/mi><\/mrow><\/msup><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mi>E<\/mi><mo stretchy=\"false\">(<\/mo><mi>X<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mi>p<\/mi><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mi>D<\/mi><mo stretchy=\"false\">(<\/mo><mi>X<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mi>p<\/mi><mo stretchy=\"false\">(<\/mo><mn>1<\/mn><mo>&#x2212;<\/mo><mi>p<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/mstyle><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">\\begin{gather*}\n    X\\sim B(1,p)\\\\\n    P\\{X=k\\}=p^kq^{1-k}\\\\\n    E(X)=p\\\\\n    D(X)=p(1-p)\n\\end{gather*}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:6.059108em;vertical-align:-2.779554em;\"><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:3.279554em;\"><span style=\"top:-5.439554em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x223C;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.05017em;\">B<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mclose\">)<\/span><\/span><\/span><span style=\"top:-3.880446em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mopen\">{<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03148em;\">k<\/span><span class=\"mclose\">}<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8991079999999999em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.03148em;\">k<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8991079999999999em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><span class=\"mbin mtight\">&#x2212;<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right:0.03148em;\">k<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-2.380446em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.05764em;\">E<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\">p<\/span><\/span><\/span><span style=\"top:-0.8804460000000001em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.02778em;\">D<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:2.779554em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h3 class=\"mume-header\" id=\"%E4%BA%8C%E9%A1%B9%E5%88%86%E5%B8%83\">&#x4E8C;&#x9879;&#x5206;&#x5E03;<\/h3>\n\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mtable rowspacing=\"0.2500em\" columnalign=\"center\" columnspacing=\"0em\"><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mi>X<\/mi><mo>&#x223C;<\/mo><mi>B<\/mi><mo stretchy=\"false\">(<\/mo><mi>n<\/mi><mo separator=\"true\">,<\/mo><mi>p<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mi>P<\/mi><mo stretchy=\"false\">{<\/mo><mi>X<\/mi><mo>=<\/mo><mi>k<\/mi><mo stretchy=\"false\">}<\/mo><mo>=<\/mo><msubsup><mi>C<\/mi><mi>n<\/mi><mi>k<\/mi><\/msubsup><msup><mi>p<\/mi><mi>k<\/mi><\/msup><mo stretchy=\"false\">(<\/mo><mn>1<\/mn><mo>&#x2212;<\/mo><mi>p<\/mi><msup><mo stretchy=\"false\">)<\/mo><mrow><mi>n<\/mi><mo>&#x2212;<\/mo><mi>k<\/mi><\/mrow><\/msup><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mi>E<\/mi><mo stretchy=\"false\">(<\/mo><mi>X<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mi>n<\/mi><mi>p<\/mi><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mi>D<\/mi><mo stretchy=\"false\">(<\/mo><mi>X<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mi>n<\/mi><mi>p<\/mi><mo stretchy=\"false\">(<\/mo><mn>1<\/mn><mo>&#x2212;<\/mo><mi>p<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/mstyle><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">\\begin{gather*}\n    X\\sim B(n,p)\\\\\n    P\\{X=k\\}=C_{n}^{k} p^{k}(1-p)^{n-k}\\\\\n    E(X)=np\\\\\n    D(X)=np(1-p)\n\\end{gather*}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:6.059108em;vertical-align:-2.779554em;\"><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:3.279554em;\"><span style=\"top:-5.439554em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x223C;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.05017em;\">B<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mclose\">)<\/span><\/span><\/span><span style=\"top:-3.880446em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mopen\">{<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03148em;\">k<\/span><span class=\"mclose\">}<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.07153em;\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8991079999999998em;\"><span style=\"top:-2.4530000000000003em;margin-left:-0.07153em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.03148em;\">k<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.247em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8991079999999999em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.03148em;\">k<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8991079999999999em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><span class=\"mbin mtight\">&#x2212;<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right:0.03148em;\">k<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-2.380446em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.05764em;\">E<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mord mathnormal\">p<\/span><\/span><\/span><span style=\"top:-0.8804460000000001em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.02778em;\">D<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:2.779554em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h4 class=\"mume-header\" id=\"%E4%BA%8C%E9%A1%B9%E5%88%86%E5%B8%83%E7%9A%84%E6%9C%80%E5%A4%A7%E5%8F%AF%E8%83%BD%E6%AC%A1%E6%95%B0-k_0\">&#x4E8C;&#x9879;&#x5206;&#x5E03;&#x7684;&#x6700;&#x5927;&#x53EF;&#x80FD;&#x6B21;&#x6570; <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>k<\/mi><mn>0<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">k_0<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.84444em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03148em;\">k<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.30110799999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.03148em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/h4>\n\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mrow><mi>P<\/mi><mo stretchy=\"false\">{<\/mo><mi>X<\/mi><mo>=<\/mo><mi>k<\/mi><mo stretchy=\"false\">}<\/mo><\/mrow><mrow><mi>P<\/mi><mo stretchy=\"false\">{<\/mo><mi>X<\/mi><mo>=<\/mo><mi>k<\/mi><mo>&#x2212;<\/mo><mn>1<\/mn><mo stretchy=\"false\">}<\/mo><\/mrow><\/mfrac><mo>=<\/mo><mrow><mo fence=\"true\">{<\/mo><mtable rowspacing=\"0.3600em\" columnalign=\"left left\" columnspacing=\"1em\"><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mrow><mo>&gt;<\/mo><mn>1<\/mn><mo separator=\"true\">,<\/mo><\/mrow><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mrow><mi>k<\/mi><mo>&lt;<\/mo><mo stretchy=\"false\">(<\/mo><mi>n<\/mi><mo>+<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><mi>p<\/mi><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mrow><mo>=<\/mo><mn>1<\/mn><mo separator=\"true\">,<\/mo><\/mrow><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mrow><mi>k<\/mi><mo>=<\/mo><mo stretchy=\"false\">(<\/mo><mi>n<\/mi><mo>+<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><mi>p<\/mi><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mrow><mo>&lt;<\/mo><mn>1<\/mn><mo separator=\"true\">,<\/mo><\/mrow><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mrow><mi>k<\/mi><mo>&gt;<\/mo><mo stretchy=\"false\">(<\/mo><mi>n<\/mi><mo>+<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><mi>p<\/mi><\/mrow><\/mstyle><\/mtd><\/mtr><\/mtable><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{P\\{X=k\\}}{P\\{X=k-1\\}}= \\begin{cases}&gt;1, &amp; k&lt;(n+1) p \\\\ =1, &amp; k=(n+1) p \\\\ &lt;1, &amp; k&gt;(n+1) p\\end{cases}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:2.363em;vertical-align:-0.936em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.427em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mopen\">{<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03148em;\">k<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mclose\">}<\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mopen\">{<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03148em;\">k<\/span><span class=\"mclose\">}<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.936em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:4.32em;vertical-align:-1.9099999999999997em;\"><\/span><span class=\"minner\"><span class=\"mopen\"><span class=\"delimsizing mult\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:2.3500199999999998em;\"><span style=\"top:-2.19999em;\"><span class=\"pstrut\" style=\"height:3.15em;\"><\/span><span class=\"delimsizinginner delim-size4\"><span>&#x23A9;<\/span><\/span><\/span><span style=\"top:-2.19199em;\"><span class=\"pstrut\" style=\"height:3.15em;\"><\/span><span style=\"height:0.31599999999999984em;width:0.889em;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"0.889em\" height=\"0.31599999999999984em\" style=\"width:0.889em\" viewBox=\"0 0 889 316\" preserveAspectRatio=\"xMinYMin\"><path d=\"M384 0 H504 V316 H384z M384 0 H504 V316 H384z\"\/><\/svg><\/span><\/span><span style=\"top:-3.15001em;\"><span class=\"pstrut\" style=\"height:3.15em;\"><\/span><span class=\"delimsizinginner delim-size4\"><span>&#x23A8;<\/span><\/span><\/span><span style=\"top:-4.292009999999999em;\"><span class=\"pstrut\" style=\"height:3.15em;\"><\/span><span style=\"height:0.31599999999999984em;width:0.889em;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"0.889em\" height=\"0.31599999999999984em\" style=\"width:0.889em\" viewBox=\"0 0 889 316\" preserveAspectRatio=\"xMinYMin\"><path d=\"M384 0 H504 V316 H384z M384 0 H504 V316 H384z\"\/><\/svg><\/span><\/span><span style=\"top:-4.600019999999999em;\"><span class=\"pstrut\" style=\"height:3.15em;\"><\/span><span class=\"delimsizinginner delim-size4\"><span>&#x23A7;<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.8500199999999998em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-l\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:2.41em;\"><span style=\"top:-4.41em;\"><span class=\"pstrut\" style=\"height:3.008em;\"><\/span><span class=\"mord\"><span class=\"mrel\">&gt;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><\/span><\/span><span style=\"top:-2.97em;\"><span class=\"pstrut\" style=\"height:3.008em;\"><\/span><span class=\"mord\"><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><\/span><\/span><span style=\"top:-1.5300000000000002em;\"><span class=\"pstrut\" style=\"height:3.008em;\"><\/span><span class=\"mord\"><span class=\"mrel\">&lt;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.9099999999999997em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width:1em;\"><\/span><span class=\"col-align-l\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:2.41em;\"><span style=\"top:-4.41em;\"><span class=\"pstrut\" style=\"height:3.008em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03148em;\">k<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&lt;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\">p<\/span><\/span><\/span><span style=\"top:-2.97em;\"><span class=\"pstrut\" style=\"height:3.008em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03148em;\">k<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\">p<\/span><\/span><\/span><span style=\"top:-1.5300000000000002em;\"><span class=\"pstrut\" style=\"height:3.008em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03148em;\">k<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&gt;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\">p<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.9099999999999997em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><br>\n<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mtext>&#x82E5;<\/mtext><mo stretchy=\"false\">(<\/mo><mi>&#x1D45B;<\/mi><mo>+<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><mi>&#x1D45D;<\/mi><mtext>&#x662F;&#x6574;&#x6570;&#xFF0C;&#x5219;<\/mtext><msub><mi>&#x1D458;<\/mi><mn>0<\/mn><\/msub><mo>=<\/mo><mo stretchy=\"false\">(<\/mo><mi>&#x1D45B;<\/mi><mo>+<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><mi>&#x1D45D;<\/mi><mtext>&#x6216;<\/mtext><mi>&#x1D45B;<\/mi><mo>+<\/mo><mn>1<\/mn><mi>&#x1D45D;<\/mi><mo>&#x2212;<\/mo><mn>1<\/mn><mspace linebreak=\"newline\"><\/mspace><mtext>&#x82E5;<\/mtext><mo stretchy=\"false\">(<\/mo><mi>&#x1D45B;<\/mi><mo>+<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><mi>&#x1D45D;<\/mi><mtext>&#x4E0D;&#x662F;&#x6574;&#x6570;&#xFF0C;&#x5219;<\/mtext><msub><mi>&#x1D458;<\/mi><mn>0<\/mn><\/msub><mo>=<\/mo><mo stretchy=\"false\">[<\/mo><mo stretchy=\"false\">(<\/mo><mi>&#x1D45B;<\/mi><mo>+<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><mi>&#x1D45D;<\/mi><mo stretchy=\"false\">]<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">&#x82E5;(&#x1D45B;+1)&#x1D45D;&#x662F;&#x6574;&#x6570;&#xFF0C;&#x5219;&#x1D458;_0=(&#x1D45B;+1)&#x1D45D;&#x6216;&#x1D45B;+1&#x1D45D;&#x2212;1\\\\\n&#x82E5;(&#x1D45B;+1)&#x1D45D;&#x4E0D;&#x662F;&#x6574;&#x6570;&#xFF0C;&#x5219;&#x1D458;_0=[(&#x1D45B;+1)&#x1D45D;]<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord cjk_fallback\">&#x82E5;<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mord cjk_fallback\">&#x662F;&#x6574;&#x6570;&#xFF0C;&#x5219;<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03148em;\">k<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.30110799999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.03148em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mord cjk_fallback\">&#x6216;<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.8388800000000001em;vertical-align:-0.19444em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.64444em;vertical-align:0em;\"><\/span><span class=\"mord\">1<\/span><\/span><span class=\"mspace newline\"><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord cjk_fallback\">&#x82E5;<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mord cjk_fallback\">&#x4E0D;&#x662F;&#x6574;&#x6570;&#xFF0C;&#x5219;<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03148em;\">k<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.30110799999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.03148em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mopen\">[(<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span><\/p>\n<h3 class=\"mume-header\" id=\"poisson-%E5%88%86%E5%B8%83\">Poisson &#x5206;&#x5E03;<\/h3>\n\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mtable rowspacing=\"0.2500em\" columnalign=\"center\" columnspacing=\"0em\"><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mi>X<\/mi><mo>&#x223C;<\/mo><mi>&#x3C0;<\/mi><mo stretchy=\"false\">(<\/mo><mi>&#x3BB;<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mi>P<\/mi><mo stretchy=\"false\">{<\/mo><mi>X<\/mi><mo>=<\/mo><mi>k<\/mi><mo stretchy=\"false\">}<\/mo><mo>=<\/mo><mfrac><msup><mi>&#x3BB;<\/mi><mi>k<\/mi><\/msup><mrow><mi>k<\/mi><mo stretchy=\"false\">!<\/mo><\/mrow><\/mfrac><msup><mi>e<\/mi><mrow><mo>&#x2212;<\/mo><mi>&#x3BB;<\/mi><\/mrow><\/msup><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mi>E<\/mi><mo stretchy=\"false\">(<\/mo><mi>X<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mi>&#x3BB;<\/mi><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mi>D<\/mi><mo stretchy=\"false\">(<\/mo><mi>X<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mi>&#x3BB;<\/mi><\/mrow><\/mstyle><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">\\begin{gather*}\n    X\\sim \\pi(\\lambda)\\\\\n    P\\{X=k\\}=\\frac{\\lambda^{k}}{k !} e^{-\\lambda}\\\\\n    E(X)=\\lambda\\\\\n    D(X)=\\lambda\n\\end{gather*}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:7.012108em;vertical-align:-3.256054em;\"><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:3.756054em;\"><span style=\"top:-6.442162em;\"><span class=\"pstrut\" style=\"height:3.526108em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x223C;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">&#x3C0;<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">&#x3BB;<\/span><span class=\"mclose\">)<\/span><\/span><\/span><span style=\"top:-4.256053999999999em;\"><span class=\"pstrut\" style=\"height:3.526108em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mopen\">{<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03148em;\">k<\/span><span class=\"mclose\">}<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.526108em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03148em;\">k<\/span><span class=\"mclose\">!<\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\">&#x3BB;<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.849108em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.03148em;\">k<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.686em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8991079999999999em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">&#x2212;<\/span><span class=\"mord mathnormal mtight\">&#x3BB;<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-2.4300539999999997em;\"><span class=\"pstrut\" style=\"height:3.526108em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.05764em;\">E<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\">&#x3BB;<\/span><\/span><\/span><span style=\"top:-0.9300540000000002em;\"><span class=\"pstrut\" style=\"height:3.526108em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.02778em;\">D<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\">&#x3BB;<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:3.256054em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h4 class=\"mume-header\" id=\"poisson-%E5%AE%9A%E7%90%86\">Poisson &#x5B9A;&#x7406;<\/h4>\n\n<p>&#x82E5;<br>\n<span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mtable rowspacing=\"0.2500em\" columnalign=\"center\" columnspacing=\"0em\"><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><msub><mi>X<\/mi><mi>n<\/mi><\/msub><mo>&#x223C;<\/mo><mi>B<\/mi><mo stretchy=\"false\">(<\/mo><mi>n<\/mi><mo separator=\"true\">,<\/mo><msub><mi>p<\/mi><mi>n<\/mi><\/msub><mo stretchy=\"false\">)<\/mo><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><munder><mrow><mi>lim<\/mi><mo>&#x2061;<\/mo><\/mrow><mrow><mi>n<\/mi><mo>&#x2192;<\/mo><mi mathvariant=\"normal\">&#x221E;<\/mi><\/mrow><\/munder><mi>n<\/mi><msub><mi>p<\/mi><mi>n<\/mi><\/msub><mo>=<\/mo><mi>&#x3BB;<\/mi><mo>&gt;<\/mo><mn>0<\/mn><\/mrow><\/mstyle><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">\\begin{gather*}\n    X_n\\sim B(n,p_n)\\\\\n    \\lim_{n\\rightarrow\\infty}np_n=\\lambda&gt;0\n\\end{gather*}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:3.3400000000000003em;vertical-align:-1.4200000000000002em;\"><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.9200000000000002em;\"><span style=\"top:-4.08em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.151392em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x223C;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.05017em;\">B<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.151392em;\"><span style=\"top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><span style=\"top:-2.58em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.69444em;\"><span style=\"top:-2.4em;margin-left:0em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><span class=\"mrel mtight\">&#x2192;<\/span><span class=\"mord mtight\">&#x221E;<\/span><\/span><\/span><\/span><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span><span class=\"mop\">lim<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mord\"><span class=\"mord mathnormal\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.151392em;\"><span style=\"top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\">&#x3BB;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&gt;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.4200000000000002em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><br>\n&#x5219;<br>\n<span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mtable rowspacing=\"0.2500em\" columnalign=\"center\" columnspacing=\"0em\"><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><munder><mrow><mi>lim<\/mi><mo>&#x2061;<\/mo><\/mrow><mrow><mi>n<\/mi><mo>&#x2192;<\/mo><mi mathvariant=\"normal\">&#x221E;<\/mi><\/mrow><\/munder><mi>P<\/mi><mrow><mo fence=\"true\">{<\/mo><msub><mi>X<\/mi><mi>n<\/mi><\/msub><mo>=<\/mo><mi>k<\/mi><mo fence=\"true\">}<\/mo><\/mrow><mo>=<\/mo><munder><mrow><mi>lim<\/mi><mo>&#x2061;<\/mo><\/mrow><mrow><mi>n<\/mi><mo>&#x2192;<\/mo><mi mathvariant=\"normal\">&#x221E;<\/mi><\/mrow><\/munder><msubsup><mi>C<\/mi><mi>n<\/mi><mi>k<\/mi><\/msubsup><msubsup><mi>p<\/mi><mi>n<\/mi><mi>k<\/mi><\/msubsup><msup><mrow><mo fence=\"true\">(<\/mo><mn>1<\/mn><mo>&#x2212;<\/mo><msub><mi>p<\/mi><mi>n<\/mi><\/msub><mo fence=\"true\">)<\/mo><\/mrow><mrow><mi>n<\/mi><mo>&#x2212;<\/mo><mi>k<\/mi><\/mrow><\/msup><mo>=<\/mo><mfrac><msup><mi>&#x3BB;<\/mi><mi>k<\/mi><\/msup><mrow><mi>k<\/mi><mo stretchy=\"false\">!<\/mo><\/mrow><\/mfrac><msup><mi>e<\/mi><mrow><mo>&#x2212;<\/mo><mi>&#x3BB;<\/mi><\/mrow><\/msup><\/mrow><\/mstyle><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">\\begin{gather*}\n    \\lim _{n \\rightarrow \\infty} P\\left\\{X_{n}=k\\right\\}=\\lim _{n \\rightarrow \\infty} C_{n}^{k} p_{n}^{k}\\left(1-p_{n}\\right)^{n-k}=\\frac{\\lambda^{k}}{k !} e^{-\\lambda}\n\\end{gather*}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:2.526108em;vertical-align:-1.0130540000000001em;\"><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.5130539999999997em;\"><span style=\"top:-3.5130539999999995em;\"><span class=\"pstrut\" style=\"height:3.526108em;\"><\/span><span class=\"mord\"><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.69444em;\"><span style=\"top:-2.4em;margin-left:0em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><span class=\"mrel mtight\">&#x2192;<\/span><span class=\"mord mtight\">&#x221E;<\/span><\/span><\/span><\/span><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span><span class=\"mop\">lim<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">{<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.151392em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03148em;\">k<\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">}<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.69444em;\"><span style=\"top:-2.4em;margin-left:0em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><span class=\"mrel mtight\">&#x2192;<\/span><span class=\"mord mtight\">&#x221E;<\/span><\/span><\/span><\/span><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span><span class=\"mop\">lim<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.07153em;\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8991079999999998em;\"><span style=\"top:-2.4530000000000003em;margin-left:-0.07153em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.03148em;\">k<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.247em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8991079999999998em;\"><span style=\"top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.03148em;\">k<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.247em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"minner\"><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.151392em;\"><span style=\"top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9890079999999999em;\"><span style=\"top:-3.2029em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><span class=\"mbin mtight\">&#x2212;<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right:0.03148em;\">k<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.526108em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03148em;\">k<\/span><span class=\"mclose\">!<\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\">&#x3BB;<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.849108em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.03148em;\">k<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.686em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8991079999999999em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">&#x2212;<\/span><span class=\"mord mathnormal mtight\">&#x3BB;<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.0130540000000001em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h3 class=\"mume-header\" id=\"%E5%87%A0%E4%BD%95%E5%88%86%E5%B8%83\">&#x51E0;&#x4F55;&#x5206;&#x5E03;<\/h3>\n\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mtable rowspacing=\"0.2500em\" columnalign=\"center\" columnspacing=\"0em\"><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mi>X<\/mi><mo>&#x223C;<\/mo><mi>G<\/mi><mo stretchy=\"false\">(<\/mo><mi>p<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mi>P<\/mi><mo stretchy=\"false\">{<\/mo><mi>X<\/mi><mo>=<\/mo><mi>k<\/mi><mo stretchy=\"false\">}<\/mo><mo>=<\/mo><mo stretchy=\"false\">(<\/mo><mn>1<\/mn><mo>&#x2212;<\/mo><mi>p<\/mi><msup><mo stretchy=\"false\">)<\/mo><mrow><mi>k<\/mi><mo>&#x2212;<\/mo><mn>1<\/mn><\/mrow><\/msup><mi>p<\/mi><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mi>E<\/mi><mo stretchy=\"false\">(<\/mo><mi>X<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>1<\/mn><mi>p<\/mi><\/mfrac><\/mrow><\/mstyle><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">\\begin{gather*}\n    X\\sim G(p)\\\\\n    P\\{X=k\\}=(1-p)^{k-1}p\\\\\n    E(X)=\\frac{1}{p}\n\\end{gather*}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:5.560988em;vertical-align:-2.530494em;\"><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:3.030494em;\"><span style=\"top:-5.511934em;\"><span class=\"pstrut\" style=\"height:3.32144em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x223C;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\">G<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mclose\">)<\/span><\/span><\/span><span style=\"top:-3.952826em;\"><span class=\"pstrut\" style=\"height:3.32144em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mopen\">{<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03148em;\">k<\/span><span class=\"mclose\">}<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8991079999999999em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.03148em;\">k<\/span><span class=\"mbin mtight\">&#x2212;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mathnormal\">p<\/span><\/span><\/span><span style=\"top:-1.971386em;\"><span class=\"pstrut\" style=\"height:3.32144em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.05764em;\">E<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.32144em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">p<\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8804400000000001em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:2.530494em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h3 class=\"mume-header\" id=\"%E8%B6%85%E5%87%A0%E4%BD%95%E5%88%86%E5%B8%83\">&#x8D85;&#x51E0;&#x4F55;&#x5206;&#x5E03;<\/h3>\n\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mtable rowspacing=\"0.2500em\" columnalign=\"center\" columnspacing=\"0em\"><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mi>P<\/mi><mo stretchy=\"false\">{<\/mo><mi>X<\/mi><mo>=<\/mo><mi>k<\/mi><mo stretchy=\"false\">}<\/mo><mo>=<\/mo><mfrac><mrow><msubsup><mi>C<\/mi><mi>M<\/mi><mi>k<\/mi><\/msubsup><msubsup><mi>C<\/mi><mrow><mi>N<\/mi><mo>&#x2212;<\/mo><mi>M<\/mi><\/mrow><mrow><mi>n<\/mi><mo>&#x2212;<\/mo><mi>k<\/mi><\/mrow><\/msubsup><\/mrow><msubsup><mi>C<\/mi><mi>N<\/mi><mi>n<\/mi><\/msubsup><\/mfrac><\/mrow><\/mstyle><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">\\begin{gather*}\n    P\\{X=k\\}=\\frac{C_M^kC_{N-M}^{n-k}}{C_N^n}\n\\end{gather*}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:2.910632em;vertical-align:-1.205316em;\"><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.705316em;\"><span style=\"top:-3.7053160000000003em;\"><span class=\"pstrut\" style=\"height:3.631101em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mopen\">{<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03148em;\">k<\/span><span class=\"mclose\">}<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.6311010000000001em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.07153em;\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.6461920000000001em;\"><span style=\"top:-2.4064690000000004em;margin-left:-0.07153em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.10903em;\">N<\/span><\/span><\/span><span style=\"top:-3.0448000000000004em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.29353099999999993em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.7418620000000002em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.07153em;\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.849108em;\"><span style=\"top:-2.424669em;margin-left:-0.07153em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.10903em;\">M<\/span><\/span><\/span><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.03148em;\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.275331em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.07153em;\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8892389999999999em;\"><span style=\"top:-2.406469em;margin-left:-0.07153em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.10903em;\">N<\/span><span class=\"mbin mtight\">&#x2212;<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right:0.10903em;\">M<\/span><\/span><\/span><\/span><span style=\"top:-3.1031310000000003em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><span class=\"mbin mtight\">&#x2212;<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right:0.03148em;\">k<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.351862em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9795309999999999em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.205316em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><br>\nN &#x4EF6;&#x4EA7;&#x54C1;&#x4E2D; M &#x4E2A;&#x6B21;&#x54C1;&#xFF0C;&#x62BD; n &#x4E2A;&#x6070;&#x597D;&#x542B; k &#x4E2A;&#x6B21;&#x54C1;&#x7684;&#x6982;&#x7387;&#x3002;<\/p>\n<h2 class=\"mume-header\" id=\"%E5%88%86%E5%B8%83%E5%87%BD%E6%95%B0-fx\">&#x5206;&#x5E03;&#x51FD;&#x6570; F(x)<\/h2>\n\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>F<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mi>P<\/mi><mo stretchy=\"false\">{<\/mo><mi>X<\/mi><mo>&#x2264;<\/mo><mi>x<\/mi><mo stretchy=\"false\">}<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">F(x)=P\\{X\\le x\\}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">F<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mopen\">{<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x2264;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">}<\/span><\/span><\/span><\/span><\/span><br>\n&#x6027;&#x8D28;&#xFF1A;<\/p>\n<ol>\n<li>&#x4E0D;&#x51CF;<\/li>\n<li><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>0<\/mn><mo>&#x2264;<\/mo><mi>F<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><mo>&#x2264;<\/mo><mn>1<\/mn><mspace linebreak=\"newline\"><\/mspace><mi>F<\/mi><mo stretchy=\"false\">(<\/mo><mo>&#x2212;<\/mo><mi mathvariant=\"normal\">&#x221E;<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>0<\/mn><mspace linebreak=\"newline\"><\/mspace><mi>F<\/mi><mo stretchy=\"false\">(<\/mo><mi mathvariant=\"normal\">&#x221E;<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">0\\le F(x)\\le1\\\\F(-\\infty)=0\\\\F(\\infty)=1<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.78041em;vertical-align:-0.13597em;\"><\/span><span class=\"mord\">0<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x2264;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">F<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x2264;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.64444em;vertical-align:0em;\"><\/span><span class=\"mord\">1<\/span><\/span><span class=\"mspace newline\"><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">F<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">&#x2212;<\/span><span class=\"mord\">&#x221E;<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.64444em;vertical-align:0em;\"><\/span><span class=\"mord\">0<\/span><\/span><span class=\"mspace newline\"><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">F<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">&#x221E;<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.64444em;vertical-align:0em;\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span><\/li>\n<li>&#x53F3;&#x8FDE;&#x7EED;<span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>F<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo>+<\/mo><mn>0<\/mn><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mi>F<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">F(x+0)=F(x)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">F<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\">0<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">F<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/li>\n<\/ol>\n<h2 class=\"mume-header\" id=\"%E6%A6%82%E7%8E%87%E5%AF%86%E5%BA%A6-fx\">&#x6982;&#x7387;&#x5BC6;&#x5EA6; f(x)<\/h2>\n\n<p>&#x5145;&#x8981;&#x6761;&#x4EF6;&#xFF1A;<\/p>\n<ol>\n<li>&#x975E;&#x8D1F;&#x6027;<span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>f<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><mo>&gt;<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">f(x)&gt;0<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&gt;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.64444em;vertical-align:0em;\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span><\/li>\n<li>&#x5F52;&#x4E00;&#x5316;<span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msubsup><mo>&#x222B;<\/mo><mrow><mo>&#x2212;<\/mo><mi mathvariant=\"normal\">&#x221E;<\/mi><\/mrow><mi mathvariant=\"normal\">&#x221E;<\/mi><\/msubsup><mi>f<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><mtext>&#xA0;<\/mtext><mi mathvariant=\"bold\">d<\/mi><mi>x<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\int_{-\\infty}^{\\infty}f(x)~\\mathbf{d}x=1<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:2.384573em;vertical-align:-0.970281em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol large-op\" style=\"margin-right:0.44445em;position:relative;top:-0.0011249999999999316em;\">&#x222B;<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.414292em;\"><span style=\"top:-1.7880500000000001em;margin-left:-0.44445em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">&#x2212;<\/span><span class=\"mord mtight\">&#x221E;<\/span><\/span><\/span><\/span><span style=\"top:-3.8129000000000004em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">&#x221E;<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.970281em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace nobreak\">&#xA0;<\/span><span class=\"mord mathbf\">d<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.64444em;vertical-align:0em;\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span><\/li>\n<\/ol>\n<h2 class=\"mume-header\" id=\"%E8%BF%9E%E7%BB%AD%E5%9E%8B%E9%9A%8F%E6%9C%BA%E5%8F%98%E9%87%8F\">&#x8FDE;&#x7EED;&#x578B;&#x968F;&#x673A;&#x53D8;&#x91CF;<\/h2>\n\n<h3 class=\"mume-header\" id=\"%E5%AE%9A%E4%B9%89\">&#x5B9A;&#x4E49;<\/h3>\n\n<p>&#x5982;&#x679C;&#x5BF9;&#x4E8E;&#x968F;&#x673A;&#x53D8;&#x91CF; X &#x7684;&#x5206;&#x5E03;&#x51FD;&#x6570;&#x1D439;(&#x1D465;)&#xFF0C;&#x5B58;&#x5728;&#x975E;&#x8D1F;&#x5B9E;&#x51FD;&#x6570;&#x1D453;(&#x1D465;)&#xFF0C;&#x4F7F;&#x5F97;&#x5BF9;&#x4E8E;&#x4EFB;&#x610F;&#x5B9E;&#x6570;&#x1D465;&#xFF0C;&#x6709;<br>\n<span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>F<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><msubsup><mo>&#x222B;<\/mo><mrow><mo>&#x2212;<\/mo><mi mathvariant=\"normal\">&#x221E;<\/mi><\/mrow><mi>x<\/mi><\/msubsup><mi>f<\/mi><mo stretchy=\"false\">(<\/mo><mi>t<\/mi><mo stretchy=\"false\">)<\/mo><mi>d<\/mi><mi>t<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">F(x)=\\int_{-\\infty}^{x} f(t) d t<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">F<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:2.384573em;vertical-align:-0.970281em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol large-op\" style=\"margin-right:0.44445em;position:relative;top:-0.0011249999999999316em;\">&#x222B;<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.414292em;\"><span style=\"top:-1.7880500000000001em;margin-left:-0.44445em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">&#x2212;<\/span><span class=\"mord mtight\">&#x221E;<\/span><\/span><\/span><\/span><span style=\"top:-3.8129000000000004em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.970281em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mord mathnormal\">t<\/span><\/span><\/span><\/span><\/span><br>\n&#x5219;&#x79F0; &#x1D44B; &#x4E3A;&#x8FDE;&#x7EED;&#x578B;&#x968F;&#x673A;&#x53D8;&#x91CF;&#xFF0C;&#x5176;&#x4E2D;&#x51FD;&#x6570; &#x1D453;(&#x1D465;) &#x79F0;&#x4E3A; &#x1D44B; &#x7684;&#x6982;&#x7387;&#x5BC6;&#x5EA6;&#x51FD;&#x6570;, &#x7B80;&#x79F0;&#x6982;&#x7387;&#x5BC6;&#x5EA6;&#x6216;&#x5BC6;&#x5EA6;&#x51FD;&#x6570;&#x3002;<\/p>\n<h3 class=\"mume-header\" id=\"%E6%B3%A8%E6%84%8F%E7%82%B9\">&#x6CE8;&#x610F;&#x70B9;<\/h3>\n\n<p>&#x8FDE;&#x7EED;&#x578B;&#x968F;&#x673A;&#x53D8;&#x91CF;&#x53D6;&#x4EFB;&#x4E00;&#x6307;&#x5B9A;&#x503C;&#x7684;&#x6982;&#x7387;&#x4E3A;0<\/p>\n<p>&#x1D443;(&#x1D434;)=0&#xFF0C;&#x5E76;&#x4E0D;&#x610F;&#x5473;&#x7740;&#x1D434;=&#x2205;<br>\n&#x1D443;(&#x1D435;)=1&#xFF0C;&#x5E76;&#x4E0D;&#x610F;&#x5473;&#x7740;&#x1D435;=&#x3A9;<\/p>\n<h2 class=\"mume-header\" id=\"%E5%B8%B8%E8%A7%81%E8%BF%9E%E7%BB%AD%E5%9E%8B%E9%9A%8F%E6%9C%BA%E5%8F%98%E9%87%8F%E5%88%86%E5%B8%83\">&#x5E38;&#x89C1;&#x8FDE;&#x7EED;&#x578B;&#x968F;&#x673A;&#x53D8;&#x91CF;&#x5206;&#x5E03;<\/h2>\n\n<h3 class=\"mume-header\" id=\"%E5%9D%87%E5%8C%80%E5%88%86%E5%B8%83\">&#x5747;&#x5300;&#x5206;&#x5E03;<\/h3>\n\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mtable rowspacing=\"0.2500em\" columnalign=\"center\" columnspacing=\"0em\"><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mi>X<\/mi><mo>&#x223C;<\/mo><mi>U<\/mi><mo stretchy=\"false\">[<\/mo><mi>a<\/mi><mo separator=\"true\">,<\/mo><mi>b<\/mi><mo stretchy=\"false\">]<\/mo><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mi>E<\/mi><mo stretchy=\"false\">(<\/mo><mi>X<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mrow><mi>a<\/mi><mo>+<\/mo><mi>b<\/mi><\/mrow><mn>2<\/mn><\/mfrac><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mi>D<\/mi><mo stretchy=\"false\">(<\/mo><mi>X<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mrow><mo stretchy=\"false\">(<\/mo><mi>b<\/mi><mo>&#x2212;<\/mo><mi>a<\/mi><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><\/mrow><mn>12<\/mn><\/mfrac><\/mrow><\/mstyle><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">\\begin{gather*}\n    X\\sim U[a,b]\\\\\n    E(X)=\\frac{a+b}{2}\\\\\n    D(X)=\\frac{(b-a)^2}{12}\n\\end{gather*}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:6.334548000000002em;vertical-align:-2.9172740000000013em;\"><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:3.417274em;\"><span style=\"top:-6.068382em;\"><span class=\"pstrut\" style=\"height:3.491108em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x223C;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.10903em;\">U<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mclose\">]<\/span><\/span><\/span><span style=\"top:-4.036942em;\"><span class=\"pstrut\" style=\"height:3.491108em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.05764em;\">E<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.37144em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mord mathnormal\">b<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.686em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><span style=\"top:-1.559833999999999em;\"><span class=\"pstrut\" style=\"height:3.491108em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.02778em;\">D<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.491108em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">12<\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8141079999999999em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.686em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:2.9172740000000013em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h3 class=\"mume-header\" id=\"%E6%8C%87%E6%95%B0%E5%88%86%E5%B8%83\">&#x6307;&#x6570;&#x5206;&#x5E03;<\/h3>\n\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mtable rowspacing=\"0.2500em\" columnalign=\"center\" columnspacing=\"0em\"><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mi>X<\/mi><mo>&#x223C;<\/mo><mi>E<\/mi><mo stretchy=\"false\">(<\/mo><mi>&#x3BB;<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mi>f<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mrow><mo fence=\"true\">{<\/mo><mtable rowspacing=\"0.1600em\" columnalign=\"center center\" columnspacing=\"1em\"><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mrow><mi>&#x3BB;<\/mi><msup><mi>e<\/mi><mrow><mo>&#x2212;<\/mo><mi>&#x3BB;<\/mi><mi>x<\/mi><\/mrow><\/msup><\/mrow><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mrow><mi>x<\/mi><mo>&gt;<\/mo><mn>0<\/mn><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mn>0<\/mn><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mrow><mi>x<\/mi><mo>&#x2264;<\/mo><mn>0<\/mn><\/mrow><\/mstyle><\/mtd><\/mtr><\/mtable><\/mrow><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mi>F<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mrow><mo fence=\"true\">{<\/mo><mtable rowspacing=\"0.1600em\" columnalign=\"center center\" columnspacing=\"1em\"><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mrow><mn>0<\/mn><mo separator=\"true\">,<\/mo><\/mrow><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mrow><mi>x<\/mi><mo>&#x2264;<\/mo><mn>0<\/mn><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mrow><mn>1<\/mn><mo>&#x2212;<\/mo><msup><mi>e<\/mi><mrow><mo>&#x2212;<\/mo><mi>&#x3BB;<\/mi><mi>x<\/mi><\/mrow><\/msup><mo separator=\"true\">,<\/mo><\/mrow><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mrow><mi>x<\/mi><mo>&gt;<\/mo><mn>0<\/mn><\/mrow><\/mstyle><\/mtd><\/mtr><\/mtable><\/mrow><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mi>E<\/mi><mo stretchy=\"false\">(<\/mo><mi>X<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>1<\/mn><mi>&#x3BB;<\/mi><\/mfrac><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mi>D<\/mi><mo stretchy=\"false\">(<\/mo><mi>X<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>1<\/mn><msup><mi>&#x3BB;<\/mi><mn>2<\/mn><\/msup><\/mfrac><\/mrow><\/mstyle><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">\\begin{gather*}\nX\\sim E(\\lambda)\\\\\n    f(x)=\\left\\{\\begin{array}{cc}\n\\lambda e^{-\\lambda x} &amp; x&gt;0 \\\\\n0 &amp; x \\leq 0\n\\end{array}\\right.\\\\\nF(x)=\\left\\{\\begin{array}{cc}\n0, &amp; x \\leq 0 \\\\\n1-e^{-\\lambda x}, &amp; x&gt;0\n\\end{array}\\right.\\\\\nE(X)=\\frac{1}{\\lambda}\\\\\nD(X)=\\frac{1}{\\lambda^2}\n\\end{gather*}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:11.533095999999999em;vertical-align:-5.5165479999999985em;\"><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:6.016548em;\"><span style=\"top:-8.631102em;\"><span class=\"pstrut\" style=\"height:3.454554em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x223C;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.05764em;\">E<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">&#x3BB;<\/span><span class=\"mclose\">)<\/span><\/span><\/span><span style=\"top:-6.516548em;\"><span class=\"pstrut\" style=\"height:3.454554em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\"><span class=\"delimsizing size3\">{<\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"arraycolsep\" style=\"width:0.5em;\"><\/span><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.454554em;\"><span style=\"top:-3.6054459999999997em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">&#x3BB;<\/span><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8491079999999999em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">&#x2212;<\/span><span class=\"mord mathnormal mtight\">&#x3BB;<\/span><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-2.405446em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9545539999999999em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width:0.5em;\"><\/span><span class=\"arraycolsep\" style=\"width:0.5em;\"><\/span><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.454554em;\"><span style=\"top:-3.6054459999999997em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&gt;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><span style=\"top:-2.405446em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x2264;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9545539999999999em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width:0.5em;\"><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><span style=\"top:-3.8074400000000006em;\"><span class=\"pstrut\" style=\"height:3.454554em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">F<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\"><span class=\"delimsizing size3\">{<\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"arraycolsep\" style=\"width:0.5em;\"><\/span><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.454554em;\"><span style=\"top:-3.6145539999999996em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">0<\/span><span class=\"mpunct\">,<\/span><\/span><\/span><span style=\"top:-2.405446em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8491079999999999em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">&#x2212;<\/span><span class=\"mord mathnormal mtight\">&#x3BB;<\/span><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9545539999999999em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width:0.5em;\"><\/span><span class=\"arraycolsep\" style=\"width:0.5em;\"><\/span><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.454554em;\"><span style=\"top:-3.6145539999999996em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x2264;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><span style=\"top:-2.405446em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&gt;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9545539999999999em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width:0.5em;\"><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><span style=\"top:-1.2314460000000005em;\"><span class=\"pstrut\" style=\"height:3.454554em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.05764em;\">E<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.32144em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">&#x3BB;<\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.686em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><span style=\"top:1.0759939999999983em;\"><span class=\"pstrut\" style=\"height:3.454554em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.02778em;\">D<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.32144em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\">&#x3BB;<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.740108em;\"><span style=\"top:-2.9890000000000003em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.686em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:5.5165479999999985em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h3 class=\"mume-header\" id=\"%E6%AD%A3%E6%80%81%E5%88%86%E5%B8%83\">&#x6B63;&#x6001;&#x5206;&#x5E03;<\/h3>\n\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mtable rowspacing=\"0.2500em\" columnalign=\"center\" columnspacing=\"0em\"><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mi>X<\/mi><mo>&#x223C;<\/mo><mi>N<\/mi><mo stretchy=\"false\">(<\/mo><mi>&#x3BC;<\/mi><mo separator=\"true\">,<\/mo><msup><mi>&#x3C3;<\/mi><mn>2<\/mn><\/msup><mo stretchy=\"false\">)<\/mo><\/mrow><\/mstyle><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">\\begin{gather*}\n    X\\sim N(\\mu,\\sigma^2)\\\\\n\\end{gather*}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1.524108em;vertical-align:-0.512054em;\"><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.012054em;\"><span style=\"top:-3.147946em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x223C;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.10903em;\">N<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">&#x3BC;<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">&#x3C3;<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8641079999999999em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.512054em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h4 class=\"mume-header\" id=\"%E6%A0%87%E5%87%86%E6%AD%A3%E6%80%81%E5%88%86%E5%B8%83\">&#x6807;&#x51C6;&#x6B63;&#x6001;&#x5206;&#x5E03;<\/h4>\n\n<p><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>&#x3BC;<\/mi><mo>=<\/mo><mn>0<\/mn><mo separator=\"true\">,<\/mo><mi>&#x3C3;<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\mu=0,\\sigma=1<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.625em;vertical-align:-0.19444em;\"><\/span><span class=\"mord mathnormal\">&#x3BC;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.8388800000000001em;vertical-align:-0.19444em;\"><\/span><span class=\"mord\">0<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">&#x3C3;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.64444em;vertical-align:0em;\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><br>\n&#x5BC6;&#x5EA6;&#x51FD;&#x6570;&#x548C;&#x5206;&#x5E03;&#x51FD;&#x6570;&#x7528;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>&#x3C6;<\/mi><mo stretchy=\"false\">(<\/mo><mi>&#x1D465;<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\varphi(&#x1D465;)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\">&#x3C6;<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span>&#x548C;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi mathvariant=\"normal\">&#x3A6;<\/mi><mo stretchy=\"false\">(<\/mo><mi>&#x1D465;<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\Phi(&#x1D465;)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\">&#x3A6;<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span>&#x8868;&#x793A;<\/p>\n<h4 class=\"mume-header\" id=\"3sigma%E5%87%86%E5%88%99\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>3<\/mn><mi>&#x3C3;<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">3\\sigma<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.64444em;vertical-align:0em;\"><\/span><span class=\"mord\">3<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">&#x3C3;<\/span><\/span><\/span><\/span>&#x51C6;&#x5219;<\/h4>\n\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mtable rowspacing=\"0.2500em\" columnalign=\"center\" columnspacing=\"0em\"><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mi>X<\/mi><mo>&#x223C;<\/mo><mi>N<\/mi><mo stretchy=\"false\">(<\/mo><mi>&#x3BC;<\/mi><mo separator=\"true\">,<\/mo><mi>&#x3C3;<\/mi><mo stretchy=\"false\">)<\/mo><mtext>&#x65F6;<\/mtext><mo separator=\"true\">,<\/mo><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mtable rowspacing=\"0.2500em\" columnalign=\"center\" columnspacing=\"0em\"><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi mathvariant=\"normal\">&#x2223;<\/mi><mi>X<\/mi><mo>&#x2212;<\/mo><mi>&#x3BC;<\/mi><mi mathvariant=\"normal\">&#x2223;<\/mi><mo>&#x2264;<\/mo><mi>&#x3C3;<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>0.6826<\/mn><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi mathvariant=\"normal\">&#x2223;<\/mi><mi>X<\/mi><mo>&#x2212;<\/mo><mi>&#x3BC;<\/mi><mi mathvariant=\"normal\">&#x2223;<\/mi><mo>&#x2264;<\/mo><mn>2<\/mn><mi>&#x3C3;<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>0.9544<\/mn><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi mathvariant=\"normal\">&#x2223;<\/mi><mi>X<\/mi><mo>&#x2212;<\/mo><mi>&#x3BC;<\/mi><mi mathvariant=\"normal\">&#x2223;<\/mi><mo>&#x2264;<\/mo><mn>3<\/mn><mi>&#x3C3;<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>0.9974<\/mn><\/mrow><\/mstyle><\/mtd><\/mtr><\/mtable><\/mstyle><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">\\begin{gather*}\n    X\\sim N(\\mu,\\sigma)&#x65F6;,\\\\\n    \\begin{gathered}\nP(|X-\\mu| \\leq \\sigma)=0.6826 \\\\\nP(|X-\\mu| \\leq 2 \\sigma)=0.9544 \\\\\nP(|X-\\mu| \\leq 3 \\sigma)=0.9974\n\\end{gathered}\n\\end{gather*}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:6.300000000000001em;vertical-align:-2.9000000000000004em;\"><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:3.4000000000000004em;\"><span style=\"top:-7.0600000000000005em;\"><span class=\"pstrut\" style=\"height:4.5em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x223C;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.10903em;\">N<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">&#x3BC;<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">&#x3C3;<\/span><span class=\"mclose\">)<\/span><span class=\"mord cjk_fallback\">&#x65F6;<\/span><span class=\"mpunct\">,<\/span><\/span><\/span><span style=\"top:-3.9000000000000004em;\"><span class=\"pstrut\" style=\"height:4.5em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:2.5000000000000004em;\"><span style=\"top:-4.66em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">&#x2223;<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mord mathnormal\">&#x3BC;<\/span><span class=\"mord\">&#x2223;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x2264;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">&#x3C3;<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord\">0.6826<\/span><\/span><\/span><span style=\"top:-3.16em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">&#x2223;<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mord mathnormal\">&#x3BC;<\/span><span class=\"mord\">&#x2223;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x2264;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord\">2<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">&#x3C3;<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord\">0.9544<\/span><\/span><\/span><span style=\"top:-1.6599999999999993em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">&#x2223;<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mord mathnormal\">&#x3BC;<\/span><span class=\"mord\">&#x2223;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x2264;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord\">3<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">&#x3C3;<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord\">0.9974<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:2.000000000000001em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:2.9000000000000004em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h3 class=\"mume-header\" id=\"gamma%E5%88%86%E5%B8%83\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi mathvariant=\"normal\">&#x393;<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\Gamma<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.68333em;vertical-align:0em;\"><\/span><span class=\"mord\">&#x393;<\/span><\/span><\/span><\/span>&#x5206;&#x5E03;<\/h3>\n\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mtable rowspacing=\"0.2500em\" columnalign=\"center\" columnspacing=\"0em\"><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mi>X<\/mi><mo>&#x223C;<\/mo><mi mathvariant=\"normal\">&#x393;<\/mi><mo stretchy=\"false\">(<\/mo><mi>r<\/mi><mo separator=\"true\">,<\/mo><mi>&#x3BB;<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mi>r<\/mi><mo>&gt;<\/mo><mn>0<\/mn><mtext>&#xFF0C;&#x5F62;&#x72B6;&#x53C2;&#x6570;<\/mtext><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mi>&#x3BB;<\/mi><mo>&gt;<\/mo><mn>0<\/mn><mtext>&#xFF0C;&#x5C3A;&#x5EA6;&#x53C2;&#x6570;<\/mtext><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mi>f<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mrow><mo fence=\"true\">{<\/mo><mtable rowspacing=\"0.1600em\" columnalign=\"center left\" columnspacing=\"1em\"><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mrow><mfrac><msup><mi>&#x3BB;<\/mi><mi>r<\/mi><\/msup><mrow><mi mathvariant=\"normal\">&#x393;<\/mi><mo stretchy=\"false\">(<\/mo><mi>r<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/mfrac><msup><mi>x<\/mi><mrow><mi>r<\/mi><mo>&#x2212;<\/mo><mn>1<\/mn><\/mrow><\/msup><msup><mi>e<\/mi><mrow><mo>&#x2212;<\/mo><mi>&#x3BB;<\/mi><mi>x<\/mi><\/mrow><\/msup><\/mrow><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mrow><mi>x<\/mi><mo>&gt;<\/mo><mn>0<\/mn><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mn>0<\/mn><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mrow><mi>x<\/mi><mo>&#x2264;<\/mo><mn>0<\/mn><\/mrow><\/mstyle><\/mtd><\/mtr><\/mtable><\/mrow><\/mrow><\/mstyle><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">\\begin{gather*}\n    X\\sim\\Gamma(r,\\lambda)\\\\\n    r&gt;0&#xFF0C;&#x5F62;&#x72B6;&#x53C2;&#x6570;\\\\\n    \\lambda&gt;0&#xFF0C;&#x5C3A;&#x5EA6;&#x53C2;&#x6570;\\\\\n    f(x)=\\left\\{\\begin{array}{cl}\n\\frac{\\lambda^{r}}{\\Gamma(r)} x^{r-1} e^{-\\lambda x} &amp; x&gt;0 \\\\\n0 &amp; x \\leq 0\n\\end{array}\\right.\n\\end{gather*}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:7.430980000000001em;vertical-align:-3.465490000000001em;\"><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:3.96549em;\"><span style=\"top:-6.69098em;\"><span class=\"pstrut\" style=\"height:3.5654899999999996em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x223C;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord\">&#x393;<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.02778em;\">r<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathnormal\">&#x3BB;<\/span><span class=\"mclose\">)<\/span><\/span><\/span><span style=\"top:-5.19098em;\"><span class=\"pstrut\" style=\"height:3.5654899999999996em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.02778em;\">r<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&gt;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord\">0<\/span><span class=\"mord cjk_fallback\">&#xFF0C;&#x5F62;&#x72B6;&#x53C2;&#x6570;<\/span><\/span><\/span><span style=\"top:-3.690979999999999em;\"><span class=\"pstrut\" style=\"height:3.5654899999999996em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">&#x3BB;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&gt;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord\">0<\/span><span class=\"mord cjk_fallback\">&#xFF0C;&#x5C3A;&#x5EA6;&#x53C2;&#x6570;<\/span><\/span><\/span><span style=\"top:-1.4654899999999988em;\"><span class=\"pstrut\" style=\"height:3.5654899999999996em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\"><span class=\"delimsizing size3\">{<\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"arraycolsep\" style=\"width:0.5em;\"><\/span><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.5654899999999996em;\"><span style=\"top:-3.6545099999999997em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.91098em;\"><span style=\"top:-2.655em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">&#x393;<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right:0.02778em;\">r<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.394em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">&#x3BB;<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7385428571428572em;\"><span style=\"top:-2.931em;margin-right:0.07142857142857144em;\"><span class=\"pstrut\" style=\"height:2.5em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.02778em;\">r<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.52em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8141079999999999em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.02778em;\">r<\/span><span class=\"mbin mtight\">&#x2212;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8491079999999999em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">&#x2212;<\/span><span class=\"mord mathnormal mtight\">&#x3BB;<\/span><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-2.29451em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.06549em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width:0.5em;\"><\/span><span class=\"arraycolsep\" style=\"width:0.5em;\"><\/span><span class=\"col-align-l\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.5654899999999996em;\"><span style=\"top:-3.6545099999999997em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&gt;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><span style=\"top:-2.29451em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x2264;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.06549em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width:0.5em;\"><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:3.465490000000001em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h4 class=\"mume-header\" id=\"r1%E5%8F%82%E6%95%B0%E4%B8%BA%CE%BB%E7%9A%84%E6%8C%87%E6%95%B0%E5%88%86%E5%B8%83\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>r<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">r=1<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.43056em;vertical-align:0em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.02778em;\">r<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.64444em;vertical-align:0em;\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span>&#xFF0C;&#x53C2;&#x6570;&#x4E3A;&#x1D706;&#x7684;&#x6307;&#x6570;&#x5206;&#x5E03;<\/h4>\n\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>f<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mrow><mo fence=\"true\">{<\/mo><mtable rowspacing=\"0.1600em\" columnalign=\"center center\" columnspacing=\"1em\"><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mrow><mi>&#x3BB;<\/mi><msup><mi>e<\/mi><mrow><mo>&#x2212;<\/mo><mi>&#x3BB;<\/mi><mi>x<\/mi><\/mrow><\/msup><\/mrow><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mrow><mi>x<\/mi><mo>&gt;<\/mo><mn>0<\/mn><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mn>0<\/mn><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mrow><mi>x<\/mi><mo>&#x2264;<\/mo><mn>0<\/mn><\/mrow><\/mstyle><\/mtd><\/mtr><\/mtable><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">f(x)=\\left\\{\\begin{array}{cc}\n\\lambda e^{-\\lambda x} &amp; x&gt;0 \\\\\n0 &amp; x \\leq 0\n\\end{array}\\right.<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:2.409108em;vertical-align:-0.9545539999999999em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\"><span class=\"delimsizing size3\">{<\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"arraycolsep\" style=\"width:0.5em;\"><\/span><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.454554em;\"><span style=\"top:-3.6054459999999997em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">&#x3BB;<\/span><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8491079999999999em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">&#x2212;<\/span><span class=\"mord mathnormal mtight\">&#x3BB;<\/span><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-2.405446em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9545539999999999em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width:0.5em;\"><\/span><span class=\"arraycolsep\" style=\"width:0.5em;\"><\/span><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.454554em;\"><span style=\"top:-3.6054459999999997em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&gt;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><span style=\"top:-2.405446em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x2264;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9545539999999999em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width:0.5em;\"><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h4 class=\"mume-header\" id=\"rnerlang-%E5%88%86%E5%B8%83\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>r<\/mi><mo>=<\/mo><mi>n<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">r=n<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.43056em;vertical-align:0em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.02778em;\">r<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.43056em;vertical-align:0em;\"><\/span><span class=\"mord mathnormal\">n<\/span><\/span><\/span><\/span>&#xFF0C;Erlang &#x5206;&#x5E03;<\/h4>\n\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>f<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mrow><mo fence=\"true\">{<\/mo><mtable rowspacing=\"0.1600em\" columnalign=\"center left\" columnspacing=\"1em\"><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mrow><mfrac><msup><mi>&#x3BB;<\/mi><mi>n<\/mi><\/msup><mrow><mo stretchy=\"false\">(<\/mo><mi>n<\/mi><mo>&#x2212;<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">!<\/mo><\/mrow><\/mfrac><msup><mi>x<\/mi><mrow><mi>n<\/mi><mo>&#x2212;<\/mo><mn>1<\/mn><\/mrow><\/msup><msup><mi>e<\/mi><mrow><mo>&#x2212;<\/mo><mi>&#x3BB;<\/mi><mi>x<\/mi><\/mrow><\/msup><\/mrow><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mrow><mi>x<\/mi><mo>&gt;<\/mo><mn>0<\/mn><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mn>0<\/mn><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mrow><mi>x<\/mi><mo>&#x2264;<\/mo><mn>0<\/mn><\/mrow><\/mstyle><\/mtd><\/mtr><\/mtable><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">f(x)=\\left\\{\\begin{array}{cl}\n\\frac{\\lambda^{n}}{(n-1) !}  x^{n-1} e^{-\\lambda x} &amp; x&gt;0 \\\\\n0  &amp; x \\leq 0\n\\end{array}\\right.<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:2.6309799999999997em;vertical-align:-1.06549em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\"><span class=\"delimsizing size3\">{<\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"arraycolsep\" style=\"width:0.5em;\"><\/span><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.5654899999999996em;\"><span style=\"top:-3.6545099999999997em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.91098em;\"><span style=\"top:-2.655em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">n<\/span><span class=\"mbin mtight\">&#x2212;<\/span><span class=\"mord mtight\">1<\/span><span class=\"mclose mtight\">)!<\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.394em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">&#x3BB;<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7385428571428572em;\"><span style=\"top:-2.931em;margin-right:0.07142857142857144em;\"><span class=\"pstrut\" style=\"height:2.5em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.52em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8141079999999999em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><span class=\"mbin mtight\">&#x2212;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8491079999999999em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">&#x2212;<\/span><span class=\"mord mathnormal mtight\">&#x3BB;<\/span><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-2.29451em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.06549em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width:0.5em;\"><\/span><span class=\"arraycolsep\" style=\"width:0.5em;\"><\/span><span class=\"col-align-l\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.5654899999999996em;\"><span style=\"top:-3.6545099999999997em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&gt;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><span style=\"top:-2.29451em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x2264;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.06549em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width:0.5em;\"><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h4 class=\"mume-header\" id=\"rn2-lambda12%E8%87%AA%E7%94%B1%E5%BA%A6%E4%B8%BAn%E7%9A%84chi2-%E5%88%86%E5%B8%83\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>&#x1D45F;<\/mi><mo>=<\/mo><mi>&#x1D45B;<\/mi><mi mathvariant=\"normal\">\/<\/mi><mn>2<\/mn><mo separator=\"true\">,<\/mo><mi>&#x3BB;<\/mi><mo>=<\/mo><mn>1<\/mn><mi mathvariant=\"normal\">\/<\/mi><mn>2<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">&#x1D45F;=&#x1D45B;\/2, \\lambda=1\/2<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.43056em;vertical-align:0em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.02778em;\">r<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mord\">\/2<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathnormal\">&#x3BB;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\">1\/2<\/span><\/span><\/span><\/span>&#xFF0C;&#x81EA;&#x7531;&#x5EA6;&#x4E3A;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>n<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">n<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.43056em;vertical-align:0em;\"><\/span><span class=\"mord mathnormal\">n<\/span><\/span><\/span><\/span>&#x7684;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi>&#x3C7;<\/mi><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">\\chi^2<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1.008548em;vertical-align:-0.19444em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">&#x3C7;<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8141079999999999em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>-&#x5206;&#x5E03;&#xFF0C;<\/h4>\n\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mtable rowspacing=\"0.2500em\" columnalign=\"center\" columnspacing=\"0em\"><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mi>X<\/mi><mo>&#x223C;<\/mo><msup><mi>&#x3C7;<\/mi><mn>2<\/mn><\/msup><mo stretchy=\"false\">(<\/mo><mi>n<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mi>f<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mrow><mo fence=\"true\">{<\/mo><mtable rowspacing=\"0.1600em\" columnalign=\"center left\" columnspacing=\"1em\"><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mrow><mfrac><mn>1<\/mn><mrow><msup><mn>2<\/mn><mfrac><mi>n<\/mi><mn>2<\/mn><\/mfrac><\/msup><mi mathvariant=\"normal\">&#x393;<\/mi><mrow><mo fence=\"true\">(<\/mo><mfrac><mi>n<\/mi><mn>2<\/mn><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><\/mfrac><msup><mi>x<\/mi><mrow><mfrac><mi>n<\/mi><mn>2<\/mn><\/mfrac><mo>&#x2212;<\/mo><mn>1<\/mn><\/mrow><\/msup><msup><mi>e<\/mi><mrow><mo>&#x2212;<\/mo><mfrac><mi>x<\/mi><mn>2<\/mn><\/mfrac><\/mrow><\/msup><\/mrow><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mrow><mi>x<\/mi><mo>&gt;<\/mo><mn>0<\/mn><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mn>0<\/mn><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mrow><mi>x<\/mi><mo>&#x2264;<\/mo><mn>0<\/mn><\/mrow><\/mstyle><\/mtd><\/mtr><\/mtable><\/mrow><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mi>X<\/mi><mo>&#x223C;<\/mo><mi>N<\/mi><mo stretchy=\"false\">(<\/mo><mn>0<\/mn><mo separator=\"true\">,<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><mo>&#x21D2;<\/mo><msup><mi>X<\/mi><mn>2<\/mn><\/msup><mo>&#x223C;<\/mo><msup><mi>&#x3C7;<\/mi><mn>2<\/mn><\/msup><mo stretchy=\"false\">(<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><\/mstyle><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">\\begin{gather*}\n    X\\sim\\chi^2(n)\\\\\nf(x)=\\left\\{\\begin{array}{cl}\n\\frac{1}{2^{\\frac{n}{2}} \\Gamma\\left(\\frac{n}{2}\\right)} x^{\\frac{n}{2}-1} e^{-\\frac{x}{2}} &amp; x&gt;0 \\\\\n0 &amp; x \\leq 0\n\\end{array}\\right.  \\\\\nX\\sim N(0,1)\\Rightarrow X^2\\sim \\chi^2(1)\n\\end{gather*}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:6.348246em;vertical-align:-2.9241229999999994em;\"><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:3.424123em;\"><span style=\"top:-6.310015em;\"><span class=\"pstrut\" style=\"height:3.75em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x223C;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">&#x3C7;<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8641079999999999em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mclose\">)<\/span><\/span><\/span><span style=\"top:-3.9000150000000002em;\"><span class=\"pstrut\" style=\"height:3.75em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\"><span class=\"delimsizing size4\">{<\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"arraycolsep\" style=\"width:0.5em;\"><\/span><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.7048925em;\"><span style=\"top:-3.8578124999999996em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.845108em;\"><span style=\"top:-2.439795em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.0717214285714287em;\"><span style=\"top:-3.48775em;margin-right:0.07142857142857144em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mopen nulldelimiter sizing reset-size1 size6\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8175600000000001em;\"><span style=\"top:-2.468em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><span style=\"top:-3.2255000000000003em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line mtight\" style=\"border-bottom-width:0.049em;\"><\/span><\/span><span style=\"top:-3.387em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.532em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter sizing reset-size1 size6\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mtight\">&#x393;<\/span><span class=\"minner mtight\"><span class=\"mopen sizing reset-size3 size6 mtight delimcenter\" style=\"top:0.07500000000000001em;\"><span class=\"mtight\">(<\/span><\/span><span class=\"mord mtight\"><span class=\"mopen nulldelimiter sizing reset-size3 size6\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.6915428571428572em;\"><span style=\"top:-2.656em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span style=\"top:-3.2255000000000003em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line mtight\" style=\"border-bottom-width:0.049em;\"><\/span><\/span><span style=\"top:-3.384em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.344em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter sizing reset-size3 size6\"><\/span><\/span><span class=\"mclose sizing reset-size3 size6 mtight delimcenter\" style=\"top:0.07500000000000001em;\"><span class=\"mtight\">)<\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.394em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.862705em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.84708em;\"><span style=\"top:-3.363em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mopen nulldelimiter sizing reset-size3 size6\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.6915428571428572em;\"><span style=\"top:-2.656em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span style=\"top:-3.2255000000000003em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line mtight\" style=\"border-bottom-width:0.049em;\"><\/span><\/span><span style=\"top:-3.384em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.344em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter sizing reset-size3 size6\"><\/span><\/span><span class=\"mbin mtight\">&#x2212;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.84708em;\"><span style=\"top:-3.363em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">&#x2212;<\/span><span class=\"mord mtight\"><span class=\"mopen nulldelimiter sizing reset-size3 size6\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.6915428571428572em;\"><span style=\"top:-2.656em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span style=\"top:-3.2255000000000003em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line mtight\" style=\"border-bottom-width:0.049em;\"><\/span><\/span><span style=\"top:-3.384em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.344em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter sizing reset-size3 size6\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-2.1551074999999997em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.2048925000000004em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width:0.5em;\"><\/span><span class=\"arraycolsep\" style=\"width:0.5em;\"><\/span><span class=\"col-align-l\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.7048925em;\"><span style=\"top:-3.8578124999999996em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&gt;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><span style=\"top:-2.1551074999999997em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x2264;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.2048925000000004em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width:0.5em;\"><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><span style=\"top:-1.4858770000000008em;\"><span class=\"pstrut\" style=\"height:3.75em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x223C;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.10903em;\">N<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">0<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x21D2;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8641079999999999em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x223C;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">&#x3C7;<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8641079999999999em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:2.9241229999999994em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><img src=\"https:\/\/i0.wp.com\/www.lazybirds.top\/wp-content\/uploads\/2021\/11\/mmexport1636202182466.jpg?w=840&#038;ssl=1\" alt data-recalc-dims=\"1\"><\/p>\n<h2 class=\"mume-header\" id=\"%E4%B8%A5%E6%A0%BC%E5%8D%95%E8%B0%83%E5%87%BD%E6%95%B0%E7%9A%84%E5%88%86%E5%B8%83\">&#x4E25;&#x683C;&#x5355;&#x8C03;&#x51FD;&#x6570;&#x7684;&#x5206;&#x5E03;<\/h2>\n\n<p><strong>&#x5B9A;&#x7406;<\/strong> &#x8BBE;&#x968F;&#x673A;&#x53D8;&#x91CF; <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>X<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">X<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.68333em;vertical-align:0em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><\/span><\/span><\/span> &#x5177;&#x6709;&#x6982;&#x7387;&#x5BC6;&#x5EA6;<br>\n<span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msub><mi>f<\/mi><mi>X<\/mi><\/msub><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><mo separator=\"true\">,<\/mo><mo stretchy=\"false\">(<\/mo><mo>&#x2212;<\/mo><mi mathvariant=\"normal\">&#x221E;<\/mi><mo>&lt;<\/mo><mi>x<\/mi><mo>&lt;<\/mo><mi mathvariant=\"normal\">&#x221E;<\/mi><mo stretchy=\"false\">)<\/mo><mo separator=\"true\">,<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">f_{X}(x),(-\\infty&lt;x&lt;\\infty),<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.32833099999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.07847em;\">X<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">&#x2212;<\/span><span class=\"mord\">&#x221E;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&lt;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.5782em;vertical-align:-0.0391em;\"><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&lt;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\">&#x221E;<\/span><span class=\"mclose\">)<\/span><span class=\"mpunct\">,<\/span><\/span><\/span><\/span><\/span><br>\n&#x53C8;&#x8BBE; <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>g<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">g(x)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">g<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span> &#x5904;&#x5904;&#x53EF;&#x5BFC;&#xFF0C;&#x4E14;&#x6052;&#x6709; <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi>g<\/mi><mo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">&#x2032;<\/mo><\/msup><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><mo>&gt;<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">g^{\\prime}(x)&gt;0<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1.001892em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">g<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.751892em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">&#x2032;<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&gt;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.64444em;vertical-align:0em;\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span> (&#x6216; <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo>&lt;<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">&lt;0<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.5782em;vertical-align:-0.0391em;\"><\/span><span class=\"mrel\">&lt;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.64444em;vertical-align:0em;\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span> )&#xFF0C;<br>\n&#x5219; <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>Y<\/mi><mo>=<\/mo><mi>g<\/mi><mo stretchy=\"false\">(<\/mo><mi>X<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">Y=g(X)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.68333em;vertical-align:0em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.22222em;\">Y<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">g<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span> &#x662F;&#x8FDE;&#x7EED;&#x578B;&#x968F;&#x673A;&#x53D8;&#x91CF;&#xFF0C;&#x5176;&#x6982;&#x7387;&#x5BC6;&#x5EA6;&#x4E3A; <span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msub><mi>f<\/mi><mi>Y<\/mi><\/msub><mo stretchy=\"false\">(<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mrow><mo fence=\"true\">{<\/mo><mtable rowspacing=\"0.1600em\" columnalign=\"center center\" columnspacing=\"1em\"><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mrow><msub><mi>f<\/mi><mi>X<\/mi><\/msub><mo stretchy=\"false\">[<\/mo><mi>h<\/mi><mo stretchy=\"false\">(<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">]<\/mo><mrow><mo fence=\"true\">&#x2223;<\/mo><msup><mi>h<\/mi><mo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">&#x2032;<\/mo><\/msup><mo stretchy=\"false\">(<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><mo fence=\"true\">&#x2223;<\/mo><\/mrow><mo separator=\"true\">,<\/mo><\/mrow><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mrow><mi>&#x3B1;<\/mi><mo>&lt;<\/mo><mi>y<\/mi><mo>&lt;<\/mo><mi>&#x3B2;<\/mi><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mrow><mn>0<\/mn><mo separator=\"true\">,<\/mo><\/mrow><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mtext>&#xA0;otherwise&#xA0;<\/mtext><\/mstyle><\/mtd><\/mtr><\/mtable><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">f_{Y}(y)=\\left\\{\\begin{array}{cc}f_{X}[h(y)]\\left|h^{\\prime}(y)\\right|, &amp; \\alpha&lt;y&lt;\\beta \\\\ 0, &amp; \\text { otherwise }\\end{array}\\right.<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.32833099999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:2.40003em;vertical-align:-0.95003em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\"><span class=\"delimsizing size3\">{<\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"arraycolsep\" style=\"width:0.5em;\"><\/span><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.45em;\"><span style=\"top:-3.61em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.32833099999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.07847em;\">X<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\">h<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mclose\">)]<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">&#x2223;<\/span><span class=\"mord\"><span class=\"mord mathnormal\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.751892em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">&#x2032;<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mclose\">)<\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">&#x2223;<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mpunct\">,<\/span><\/span><\/span><span style=\"top:-2.4099999999999997em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">0<\/span><span class=\"mpunct\">,<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9500000000000004em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width:0.5em;\"><\/span><span class=\"arraycolsep\" style=\"width:0.5em;\"><\/span><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.45em;\"><span style=\"top:-3.61em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">&#x3B1;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&lt;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&lt;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.05278em;\">&#x3B2;<\/span><\/span><\/span><span style=\"top:-2.4099999999999997em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord text\"><span class=\"mord\">&#xA0;otherwise&#xA0;<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9500000000000004em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width:0.5em;\"><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><br>\n&#x5176;&#x4E2D; <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>h<\/mi><mo stretchy=\"false\">(<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">h(y)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\">h<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span> &#x662F; <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>g<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">g(x)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">g<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span> &#x7684;&#x53CD;&#x51FD;&#x6570;&#xFF0C;&#x5373;<br>\n<span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>x<\/mi><mo>=<\/mo><msup><mi>g<\/mi><mrow><mo>&#x2212;<\/mo><mn>1<\/mn><\/mrow><\/msup><mo stretchy=\"false\">(<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mi>h<\/mi><mo stretchy=\"false\">(<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">x=g^{-1}(y)=h(y)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.43056em;vertical-align:0em;\"><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1.1141079999999999em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">g<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.864108em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">&#x2212;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\">h<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>&#x3B1;<\/mi><mo>=<\/mo><mi>min<\/mi><mo>&#x2061;<\/mo><mo stretchy=\"false\">{<\/mo><mi>g<\/mi><mo stretchy=\"false\">(<\/mo><mo>&#x2212;<\/mo><mi mathvariant=\"normal\">&#x221E;<\/mi><mo stretchy=\"false\">)<\/mo><mo separator=\"true\">,<\/mo><mi>g<\/mi><mo stretchy=\"false\">(<\/mo><mo>+<\/mo><mi mathvariant=\"normal\">&#x221E;<\/mi><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">}<\/mo><mo separator=\"true\">,<\/mo><mi>&#x3B2;<\/mi><mo>=<\/mo><mi>max<\/mi><mo>&#x2061;<\/mo><mo stretchy=\"false\">{<\/mo><mi>g<\/mi><mo stretchy=\"false\">(<\/mo><mo>&#x2212;<\/mo><mi mathvariant=\"normal\">&#x221E;<\/mi><mo stretchy=\"false\">)<\/mo><mo separator=\"true\">,<\/mo><mi>g<\/mi><mo stretchy=\"false\">(<\/mo><mo>+<\/mo><mi mathvariant=\"normal\">&#x221E;<\/mi><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">}<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\alpha=\\min \\{g(-\\infty), g(+\\infty)\\}, \\beta=\\max \\{g(-\\infty), g(+\\infty)\\}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.43056em;vertical-align:0em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">&#x3B1;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mop\">min<\/span><span class=\"mopen\">{<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">g<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">&#x2212;<\/span><span class=\"mord\">&#x221E;<\/span><span class=\"mclose\">)<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">g<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">+<\/span><span class=\"mord\">&#x221E;<\/span><span class=\"mclose\">)}<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.05278em;\">&#x3B2;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mop\">max<\/span><span class=\"mopen\">{<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">g<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">&#x2212;<\/span><span class=\"mord\">&#x221E;<\/span><span class=\"mclose\">)<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">g<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">+<\/span><span class=\"mord\">&#x221E;<\/span><span class=\"mclose\">)}<\/span><\/span><\/span><\/span><\/p>\n<p><strong>&#x8865;&#x5145;&#x5B9A;&#x7406;(&#x5206;&#x6BB5;&#x5355;&#x8C03;)&#xFF1A;<\/strong><br>\n&#x82E5; <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>g<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">g(x)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">g<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span> &#x5728;&#x4E0D;&#x76F8;&#x53E0;&#x7684;&#x533A;&#x95F4; <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>I<\/mi><mn>1<\/mn><\/msub><mo separator=\"true\">,<\/mo><msub><mi>I<\/mi><mn>2<\/mn><\/msub><mo separator=\"true\">,<\/mo><mo>&#x2026;<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">I_{1}, I_{2}, \\ldots<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.8777699999999999em;vertical-align:-0.19444em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">I<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.30110799999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">I<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.30110799999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"minner\">&#x2026;<\/span><\/span><\/span><\/span> &#x4E0A;&#x9010;&#x6BB5;&#x4E25;&#x683C;&#x5355;&#x8C03;&#xFF0C;&#x5176;&#x53CD;&#x51FD;&#x6570;&#x5206;&#x522B;&#x4E3A; <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>h<\/mi><mn>1<\/mn><\/msub><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><mo separator=\"true\">,<\/mo><msub><mi>h<\/mi><mn>2<\/mn><\/msub><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><mo separator=\"true\">,<\/mo><mo>&#x2026;<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">h_{1}(x), h_{2}(x), \\ldots<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.30110799999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.30110799999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"minner\">&#x2026;<\/span><\/span><\/span><\/span> &#x5747;&#x4E3A;&#x8FDE;&#x7EED;&#x51FD;&#x6570;&#xFF0C;&#x90A3;&#x4E48; <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>Y<\/mi><mo>=<\/mo><mi>g<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">Y=g(x)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.68333em;vertical-align:0em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.22222em;\">Y<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">g<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span> &#x662F;&#x8FDE;&#x7EED;&#x578B;&#x968F;&#x673A;&#x53D8;&#x91CF;&#xFF0C;&#x5176;&#x6982;&#x7387;&#x5BC6;&#x5EA6;&#x4E3A;<br>\n<span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mtable rowspacing=\"0.2500em\" columnalign=\"center\" columnspacing=\"0em\"><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><msub><mi>f<\/mi><mi>Y<\/mi><\/msub><mo stretchy=\"false\">(<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><msub><mi>f<\/mi><mi>X<\/mi><\/msub><mrow><mo fence=\"true\">[<\/mo><msub><mi>h<\/mi><mn>1<\/mn><\/msub><mo stretchy=\"false\">(<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><mo fence=\"true\">]<\/mo><\/mrow><mrow><mo fence=\"true\">&#x2223;<\/mo><msubsup><mi>h<\/mi><mn>1<\/mn><mo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">&#x2032;<\/mo><\/msubsup><mo stretchy=\"false\">(<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><mo fence=\"true\">&#x2223;<\/mo><\/mrow><mo>+<\/mo><msub><mi>f<\/mi><mi>X<\/mi><\/msub><mrow><mo fence=\"true\">[<\/mo><msub><mi>h<\/mi><mn>2<\/mn><\/msub><mo stretchy=\"false\">(<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><mo fence=\"true\">]<\/mo><\/mrow><mrow><mo fence=\"true\">&#x2223;<\/mo><msubsup><mi>h<\/mi><mn>2<\/mn><mo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">&#x2032;<\/mo><\/msubsup><mo stretchy=\"false\">(<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><mo fence=\"true\">&#x2223;<\/mo><\/mrow><mo>+<\/mo><mo>&#x22EF;<\/mo><mtext>&#x2009;<\/mtext><mo separator=\"true\">,<\/mo><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mi>y<\/mi><mo>&#x2208;<\/mo><mo stretchy=\"false\">(<\/mo><mi>&#x3B1;<\/mi><mo separator=\"true\">,<\/mo><mi>&#x3B2;<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/mstyle><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">\\begin{gathered}\nf_{Y}(y)=f_{X}\\left[h_{1}(y)\\right]\\left|h_{1}^{\\prime}(y)\\right|+f_{X}\\left[h_{2}(y)\\right]\\left|h_{2}^{\\prime}(y)\\right|+\\cdots, \\\\\ny \\in(\\alpha, \\beta)\n\\end{gathered}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:3.0000000000000004em;vertical-align:-1.2500000000000002em;\"><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.7500000000000002em;\"><span style=\"top:-3.91em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.32833099999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.32833099999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.07847em;\">X<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">[<\/span><span class=\"mord\"><span class=\"mord mathnormal\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.30110799999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mclose\">)<\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">]<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">&#x2223;<\/span><span class=\"mord\"><span class=\"mord mathnormal\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8018919999999999em;\"><span style=\"top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">&#x2032;<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.247em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mclose\">)<\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">&#x2223;<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.32833099999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.07847em;\">X<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">[<\/span><span class=\"mord\"><span class=\"mord mathnormal\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.30110799999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mclose\">)<\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">]<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">&#x2223;<\/span><span class=\"mord\"><span class=\"mord mathnormal\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8018919999999999em;\"><span style=\"top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">&#x2032;<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.247em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mclose\">)<\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">&#x2223;<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"minner\">&#x22EF;<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mpunct\">,<\/span><\/span><\/span><span style=\"top:-2.41em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x2208;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">&#x3B1;<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.05278em;\">&#x3B2;<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.2500000000000002em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h1 class=\"mume-header\" id=\"%E5%A4%9A%E7%BB%B4%E9%9A%8F%E6%9C%BA%E5%8F%98%E9%87%8F%E5%8F%8A%E5%85%B6%E5%88%86%E5%B8%83\">&#x591A;&#x7EF4;&#x968F;&#x673A;&#x53D8;&#x91CF;&#x53CA;&#x5176;&#x5206;&#x5E03;<\/h1>\n\n<h2 class=\"mume-header\" id=\"%E4%BA%8C%E7%BB%B4%E9%9A%8F%E6%9C%BA%E5%8F%98%E9%87%8F%E7%9A%84%E8%81%94%E5%90%88%E5%88%86%E5%B8%83%E5%87%BD%E6%95%B0-fxy\">&#x4E8C;&#x7EF4;&#x968F;&#x673A;&#x53D8;&#x91CF;&#x7684;&#x8054;&#x5408;&#x5206;&#x5E03;&#x51FD;&#x6570; F(x,y)<\/h2>\n\n<p>&#x5145;&#x8981;&#x6761;&#x4EF6;&#xFF1A;<\/p>\n<ol>\n<li>&#x5355;&#x8C03;<\/li>\n<li>&#x6709;&#x754C;&#xFF1A;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>0<\/mn><mo>&#x2264;<\/mo><mi>F<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo separator=\"true\">,<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><mo>&#x2264;<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">0\\le F(x,y)\\le 1<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.78041em;vertical-align:-0.13597em;\"><\/span><span class=\"mord\">0<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x2264;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">F<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x2264;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.64444em;vertical-align:0em;\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span> &#x4E14;<br>\n<span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi mathvariant=\"normal\">&#x2200;<\/mi><mi>x<\/mi><mo separator=\"true\">,<\/mo><mi>F<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo separator=\"true\">,<\/mo><mo>&#x2212;<\/mo><mi mathvariant=\"normal\">&#x221E;<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>0<\/mn><mspace linebreak=\"newline\"><\/mspace><mi mathvariant=\"normal\">&#x2200;<\/mi><mi>y<\/mi><mo separator=\"true\">,<\/mo><mi>F<\/mi><mo stretchy=\"false\">(<\/mo><mo>&#x2212;<\/mo><mi mathvariant=\"normal\">&#x221E;<\/mi><mo separator=\"true\">,<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>0<\/mn><mspace linebreak=\"newline\"><\/mspace><mi>F<\/mi><mo stretchy=\"false\">(<\/mo><mo>&#x2212;<\/mo><mi mathvariant=\"normal\">&#x221E;<\/mi><mo separator=\"true\">,<\/mo><mo>&#x2212;<\/mo><mi mathvariant=\"normal\">&#x221E;<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>0<\/mn><mspace linebreak=\"newline\"><\/mspace><mi>F<\/mi><mo stretchy=\"false\">(<\/mo><mi mathvariant=\"normal\">&#x221E;<\/mi><mo separator=\"true\">,<\/mo><mi mathvariant=\"normal\">&#x221E;<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\forall x,F(x,-\\infty)=0\\\\\\forall y,F(-\\infty,y)=0\\\\F(-\\infty,-\\infty)=0\\\\F(\\infty,\\infty)=1<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\">&#x2200;<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">F<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord\">&#x2212;<\/span><span class=\"mord\">&#x221E;<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.64444em;vertical-align:0em;\"><\/span><span class=\"mord\">0<\/span><\/span><span class=\"mspace newline\"><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\">&#x2200;<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">F<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">&#x2212;<\/span><span class=\"mord\">&#x221E;<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.64444em;vertical-align:0em;\"><\/span><span class=\"mord\">0<\/span><\/span><span class=\"mspace newline\"><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">F<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">&#x2212;<\/span><span class=\"mord\">&#x221E;<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord\">&#x2212;<\/span><span class=\"mord\">&#x221E;<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.64444em;vertical-align:0em;\"><\/span><span class=\"mord\">0<\/span><\/span><span class=\"mspace newline\"><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">F<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">&#x221E;<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord\">&#x221E;<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.64444em;vertical-align:0em;\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span><\/li>\n<li>&#x53F3;&#x8FDE;&#x7EED;<\/li>\n<li>&#x975E;&#x8D1F;&#x6027;&#xFF1A;&#x82E5; <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>x<\/mi><mn>1<\/mn><\/msub><mo>&lt;<\/mo><msub><mi>x<\/mi><mn>2<\/mn><\/msub><mo separator=\"true\">,<\/mo><msub><mi>y<\/mi><mn>1<\/mn><\/msub><mo>&lt;<\/mo><msub><mi>y<\/mi><mn>2<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">x_{1}&lt;x_{2}, y_{1}&lt;y_{2}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.6891em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.30110799999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&lt;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.7335400000000001em;vertical-align:-0.19444em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.30110799999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.30110799999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&lt;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.625em;vertical-align:-0.19444em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.30110799999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>, &#x5219; <span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>F<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi>x<\/mi><mn>2<\/mn><\/msub><mo separator=\"true\">,<\/mo><msub><mi>y<\/mi><mn>2<\/mn><\/msub><mo fence=\"true\">)<\/mo><\/mrow><mo>+<\/mo><mi>F<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi>x<\/mi><mn>1<\/mn><\/msub><mo separator=\"true\">,<\/mo><msub><mi>y<\/mi><mn>1<\/mn><\/msub><mo fence=\"true\">)<\/mo><\/mrow><mo>&#x2212;<\/mo><mi>F<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi>x<\/mi><mn>2<\/mn><\/msub><mo separator=\"true\">,<\/mo><msub><mi>y<\/mi><mn>1<\/mn><\/msub><mo fence=\"true\">)<\/mo><\/mrow><mo>&#x2212;<\/mo><mi>F<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi>x<\/mi><mn>1<\/mn><\/msub><mo separator=\"true\">,<\/mo><msub><mi>y<\/mi><mn>2<\/mn><\/msub><mo fence=\"true\">)<\/mo><\/mrow><mo>&#x2265;<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">F\\left(x_{2}, y_{2}\\right)+F\\left(x_{1}, y_{1}\\right)-F\\left(x_{2}, y_{1}\\right)-F\\left(x_{1}, y_{2}\\right) \\geq 0<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">F<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.30110799999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.30110799999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">F<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.30110799999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.30110799999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">F<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.30110799999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.30110799999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">F<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.30110799999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.30110799999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x2265;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.64444em;vertical-align:0em;\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span><\/li>\n<\/ol>\n<h2 class=\"mume-header\" id=\"%E5%A4%9A%E5%85%83%E6%AD%A3%E6%80%81%E5%88%86%E5%B8%83\">&#x591A;&#x5143;&#x6B63;&#x6001;&#x5206;&#x5E03;<\/h2>\n\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msub><mi>f<\/mi><mi mathvariant=\"bold\">x<\/mi><\/msub><mrow><mo fence=\"true\">(<\/mo><msub><mi>x<\/mi><mn>1<\/mn><\/msub><mo separator=\"true\">,<\/mo><mo>&#x2026;<\/mo><mo separator=\"true\">,<\/mo><msub><mi>x<\/mi><mi>k<\/mi><\/msub><mo fence=\"true\">)<\/mo><\/mrow><mo>=<\/mo><mfrac><mn>1<\/mn><msqrt><mrow><mo stretchy=\"false\">(<\/mo><mn>2<\/mn><mi>&#x3C0;<\/mi><msup><mo stretchy=\"false\">)<\/mo><mi>k<\/mi><\/msup><mi mathvariant=\"normal\">&#x2223;<\/mi><mi mathvariant=\"bold\">&#x3A3;<\/mi><mi mathvariant=\"normal\">&#x2223;<\/mi><\/mrow><\/msqrt><\/mfrac><msup><mi mathvariant=\"normal\">e<\/mi><mrow><mo>&#x2212;<\/mo><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mo stretchy=\"false\">(<\/mo><mi mathvariant=\"bold\">x<\/mi><mo>&#x2212;<\/mo><mi mathvariant=\"bold-italic\">&#x3BC;<\/mi><msup><mo stretchy=\"false\">)<\/mo><mi mathvariant=\"normal\">T<\/mi><\/msup><msup><mi mathvariant=\"bold\">&#x3A3;<\/mi><mrow><mo>&#x2212;<\/mo><mn>1<\/mn><\/mrow><\/msup><mo stretchy=\"false\">(<\/mo><mi mathvariant=\"bold\">x<\/mi><mo>&#x2212;<\/mo><mi mathvariant=\"bold-italic\">&#x3BC;<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">f_{\\mathbf{x}}\\left(x_{1}, \\ldots, x_{k}\\right)=\\frac{1}{\\sqrt{(2 \\pi)^{k}|\\boldsymbol{\\Sigma}|}} \\mathrm{e}^{-\\frac{1}{2}(\\mathbf{x}-\\boldsymbol{\\mu})^{\\mathrm{T}} \\boldsymbol{\\Sigma}^{-1}(\\mathbf{x}-\\boldsymbol{\\mu})}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.161108em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathbf mtight\">x<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.30110799999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"minner\">&#x2026;<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.33610799999999996em;\"><span style=\"top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.03148em;\">k<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:2.45144em;vertical-align:-1.13em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.32144em;\"><span style=\"top:-2.162446em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.947554em;\"><span class=\"svg-align\" style=\"top:-3.2em;\"><span class=\"pstrut\" style=\"height:3.2em;\"><\/span><span class=\"mord\" style=\"padding-left:1em;\"><span class=\"mopen\">(<\/span><span class=\"mord\">2<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">&#x3C0;<\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7751079999999999em;\"><span style=\"top:-2.9890000000000003em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.03148em;\">k<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">&#x2223;<\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathbf\">&#x3A3;<\/span><\/span><\/span><span class=\"mord\">&#x2223;<\/span><\/span><\/span><span style=\"top:-2.907554em;\"><span class=\"pstrut\" style=\"height:3.2em;\"><\/span><span class=\"hide-tail\" style=\"min-width:1.02em;height:1.28em;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"400em\" height=\"1.28em\" viewBox=\"0 0 400000 1296\" preserveAspectRatio=\"xMinYMin slice\"><path d=\"M263,681c0.7,0,18,39.7,52,119\nc34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120\nc340,-704.7,510.7,-1060.3,512,-1067\nl0 -0\nc4.7,-7.3,11,-11,19,-11\nH40000v40H1012.3\ns-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232\nc-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1\ns-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26\nc-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z\nM1001 80h400000v40h-400000z\"\/><\/svg><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.292446em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.13em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord\"><span class=\"mord mathrm\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.056365em;\"><span style=\"top:-3.4130000000000003em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">&#x2212;<\/span><span class=\"mord mtight\"><span class=\"mopen nulldelimiter sizing reset-size3 size6\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8443142857142858em;\"><span style=\"top:-2.656em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span style=\"top:-3.2255000000000003em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line mtight\" style=\"border-bottom-width:0.049em;\"><\/span><\/span><span style=\"top:-3.384em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.344em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter sizing reset-size3 size6\"><\/span><\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathbf mtight\">x<\/span><span class=\"mbin mtight\">&#x2212;<\/span><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord boldsymbol mtight\">&#x3BC;<\/span><\/span><\/span><span class=\"mclose mtight\"><span class=\"mclose mtight\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9190928571428572em;\"><span style=\"top:-2.931em;margin-right:0.07142857142857144em;\"><span class=\"pstrut\" style=\"height:2.5em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">T<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathbf mtight\">&#x3A3;<\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8913142857142857em;\"><span style=\"top:-2.931em;margin-right:0.07142857142857144em;\"><span class=\"pstrut\" style=\"height:2.5em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">&#x2212;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathbf mtight\">x<\/span><span class=\"mbin mtight\">&#x2212;<\/span><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord boldsymbol mtight\">&#x3BC;<\/span><\/span><\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h2 class=\"mume-header\" id=\"%E8%BE%B9%E7%BC%98%E5%88%86%E5%B8%83\">&#x8FB9;&#x7F18;&#x5206;&#x5E03;<\/h2>\n\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msub><mi>F<\/mi><mi>X<\/mi><\/msub><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mi>F<\/mi><mo stretchy=\"false\">(<\/mo><mi>X<\/mi><mo separator=\"true\">,<\/mo><mo>+<\/mo><mi mathvariant=\"normal\">&#x221E;<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><msubsup><mo>&#x222B;<\/mo><mrow><mo>&#x2212;<\/mo><mi mathvariant=\"normal\">&#x221E;<\/mi><\/mrow><mi>x<\/mi><\/msubsup><msub><mi>f<\/mi><mi>X<\/mi><\/msub><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><mtext>&#xA0;<\/mtext><mi mathvariant=\"bold\">d<\/mi><mi>x<\/mi><mspace linebreak=\"newline\"><\/mspace><msub><mi>f<\/mi><mi>X<\/mi><\/msub><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><msubsup><mo>&#x222B;<\/mo><mrow><mo>&#x2212;<\/mo><mi mathvariant=\"normal\">&#x221E;<\/mi><\/mrow><mrow><mo>+<\/mo><mi mathvariant=\"normal\">&#x221E;<\/mi><\/mrow><\/msubsup><mi>f<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo separator=\"true\">,<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><mtext>&#xA0;<\/mtext><mi mathvariant=\"bold\">d<\/mi><mi>y<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">F_X(x)=F(X,+\\infty)=\\int_{-\\infty}^xf_X(x)~\\mathbf{d}x\\\\\nf_X(x)=\\int_{-\\infty}^{+\\infty}f(x,y)~\\mathbf{d}y<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.32833099999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.07847em;\">X<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">F<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord\">+<\/span><span class=\"mord\">&#x221E;<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:2.384573em;vertical-align:-0.970281em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol large-op\" style=\"margin-right:0.44445em;position:relative;top:-0.0011249999999999316em;\">&#x222B;<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.414292em;\"><span style=\"top:-1.7880500000000001em;margin-left:-0.44445em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">&#x2212;<\/span><span class=\"mord mtight\">&#x221E;<\/span><\/span><\/span><\/span><span style=\"top:-3.8129000000000004em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.970281em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.32833099999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.07847em;\">X<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace nobreak\">&#xA0;<\/span><span class=\"mord mathbf\">d<\/span><span class=\"mord mathnormal\">x<\/span><\/span><span class=\"mspace newline\"><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.32833099999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.07847em;\">X<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:2.491512em;vertical-align:-0.970281em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol large-op\" style=\"margin-right:0.44445em;position:relative;top:-0.0011249999999999316em;\">&#x222B;<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.5212310000000002em;\"><span style=\"top:-1.7880500000000001em;margin-left:-0.44445em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">&#x2212;<\/span><span class=\"mord mtight\">&#x221E;<\/span><\/span><\/span><\/span><span style=\"top:-3.8129000000000004em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">+<\/span><span class=\"mord mtight\">&#x221E;<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.970281em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mclose\">)<\/span><span class=\"mspace nobreak\">&#xA0;<\/span><span class=\"mord mathbf\">d<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><\/span><\/span><\/span><\/span><\/p>\n<h2 class=\"mume-header\" id=\"%E6%9D%A1%E4%BB%B6%E5%88%86%E5%B8%83\">&#x6761;&#x4EF6;&#x5206;&#x5E03;<\/h2>\n\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mtable rowspacing=\"0.2500em\" columnalign=\"right left\" columnspacing=\"0em\"><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><msub><mi>F<\/mi><mrow><mi>X<\/mi><mi mathvariant=\"normal\">&#x2223;<\/mi><mi>Y<\/mi><\/mrow><\/msub><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mi mathvariant=\"normal\">&#x2223;<\/mi><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mrow><\/mrow><mo>=<\/mo><mi>P<\/mi><mo stretchy=\"false\">{<\/mo><mi>X<\/mi><mo>&lt;<\/mo><mi>x<\/mi><mi mathvariant=\"normal\">&#x2223;<\/mi><mi>Y<\/mi><mo>=<\/mo><mi>y<\/mi><mo stretchy=\"false\">}<\/mo><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><\/mrow><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mrow><\/mrow><mo>=<\/mo><munder><mrow><mi>lim<\/mi><mo>&#x2061;<\/mo><\/mrow><mrow><mi>&#x3F5;<\/mi><mo>&#x2192;<\/mo><mn>0<\/mn><\/mrow><\/munder><mi>P<\/mi><mo stretchy=\"false\">{<\/mo><mi>X<\/mi><mo>&#x2264;<\/mo><mi>x<\/mi><mo>&#x2223;<\/mo><mi>y<\/mi><mo>&lt;<\/mo><mi>Y<\/mi><mo>&#x2264;<\/mo><mi>y<\/mi><mo>+<\/mo><mi>&#x3F5;<\/mi><mo stretchy=\"false\">}<\/mo><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><\/mrow><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mrow><\/mrow><mo>=<\/mo><munder><mrow><mi>lim<\/mi><mo>&#x2061;<\/mo><\/mrow><mrow><mi>&#x3F5;<\/mi><mo>&#x2192;<\/mo><mn>0<\/mn><\/mrow><\/munder><mfrac><mrow><mi>P<\/mi><mo stretchy=\"false\">{<\/mo><mi>X<\/mi><mo>&#x2264;<\/mo><mi>x<\/mi><mo separator=\"true\">,<\/mo><mi>y<\/mi><mo>&lt;<\/mo><mi>Y<\/mi><mo>&#x2264;<\/mo><mi>y<\/mi><mo>+<\/mo><mi>&#x3F5;<\/mi><mo stretchy=\"false\">}<\/mo><\/mrow><mrow><mi>P<\/mi><mo stretchy=\"false\">{<\/mo><mi>y<\/mi><mo>&lt;<\/mo><mi>Y<\/mi><mo>&#x2264;<\/mo><mi>y<\/mi><mo>+<\/mo><mi>&#x3F5;<\/mi><mo stretchy=\"false\">}<\/mo><\/mrow><\/mfrac><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><\/mrow><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mrow><\/mrow><mo>=<\/mo><munder><mrow><mi>lim<\/mi><mo>&#x2061;<\/mo><\/mrow><mrow><mi>&#x3B5;<\/mi><mo>&#x2192;<\/mo><msup><mn>0<\/mn><mo lspace=\"0em\" rspace=\"0em\">+<\/mo><\/msup><\/mrow><\/munder><mfrac><mrow><mi>F<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo separator=\"true\">,<\/mo><mi>y<\/mi><mo>+<\/mo><mi>&#x3B5;<\/mi><mo stretchy=\"false\">)<\/mo><mo>&#x2212;<\/mo><mi>F<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo separator=\"true\">,<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><mrow><msub><mi>F<\/mi><mi>Y<\/mi><\/msub><mo stretchy=\"false\">(<\/mo><mi>y<\/mi><mo>+<\/mo><mi>&#x3B5;<\/mi><mo stretchy=\"false\">)<\/mo><mo>&#x2212;<\/mo><msub><mi>F<\/mi><mi>Y<\/mi><\/msub><mo stretchy=\"false\">(<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/mfrac><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><\/mrow><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mrow><\/mrow><mo>=<\/mo><mfrac><mrow><mfrac><mi mathvariant=\"normal\">&#x2202;<\/mi><mrow><mi mathvariant=\"normal\">&#x2202;<\/mi><mi>y<\/mi><\/mrow><\/mfrac><mi>F<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo separator=\"true\">,<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><mrow><mfrac><mi mathvariant=\"normal\">&#x2202;<\/mi><mrow><mi mathvariant=\"normal\">&#x2202;<\/mi><mi>y<\/mi><\/mrow><\/mfrac><msub><mi>F<\/mi><mi>Y<\/mi><\/msub><mo stretchy=\"false\">(<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/mfrac><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><\/mrow><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mrow><\/mrow><mo>=<\/mo><msubsup><mo>&#x222B;<\/mo><mrow><mo>&#x2212;<\/mo><mi mathvariant=\"normal\">&#x221E;<\/mi><\/mrow><mi>x<\/mi><\/msubsup><mfrac><mrow><mi>f<\/mi><mo stretchy=\"false\">(<\/mo><mi>u<\/mi><mo separator=\"true\">,<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><mrow><msub><mi>f<\/mi><mi>Y<\/mi><\/msub><mo stretchy=\"false\">(<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/mfrac><mi>d<\/mi><mi>u<\/mi><\/mrow><\/mstyle><\/mtd><\/mtr><\/mtable><mspace linebreak=\"newline\"><\/mspace><msub><mi>f<\/mi><mrow><mi>X<\/mi><mi mathvariant=\"normal\">&#x2223;<\/mi><mi>Y<\/mi><\/mrow><\/msub><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mi mathvariant=\"normal\">&#x2223;<\/mi><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mrow><mi>f<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo separator=\"true\">,<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><mrow><msub><mi>f<\/mi><mi>Y<\/mi><\/msub><mo stretchy=\"false\">(<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\begin{aligned}F_{X|Y}(x|y)&amp;=P\\{X&lt;x|Y=y\\}\\\\\n&amp;=\\lim _{\\epsilon \\rightarrow 0} P\\{X \\leq x \\mid y&lt;Y \\leq y+\\epsilon\\}\\\\\n&amp;=\\lim _{\\epsilon \\rightarrow 0} \\frac{P\\{X \\leq x, y&lt;Y \\leq y+\\epsilon\\}}{P\\{y&lt;Y \\leq y+\\epsilon\\}}\\\\\n&amp;=\\lim _{\\varepsilon \\rightarrow 0^{+}} \\frac{F(x, y+\\varepsilon)-F(x, y)}{F_{Y}(y+\\varepsilon)-F_{Y}(y)}\\\\\n&amp;=\\frac{\\frac{\\partial}{\\partial y} F(x, y)}{\\frac{\\partial}{\\partial y} F_{Y}(y)} \\\\\n&amp;=\\int_{-\\infty}^{x} \\frac{f(u, y)}{f_{Y}(y)} d u\n\\end{aligned}\\\\\nf_{X|Y}(x|y)=\\frac{f(x,y)}{f_Y(y)}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:14.682820999999999em;vertical-align:-7.0914104999999985em;\"><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-r\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:7.5914105em;\"><span style=\"top:-10.5026265em;\"><span class=\"pstrut\" style=\"height:3.751216em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.34480000000000005em;\"><span style=\"top:-2.5198em;margin-left:-0.13889em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mord mtight\">&#x2223;<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right:0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3551999999999999em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mord\">&#x2223;<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mclose\">)<\/span><\/span><\/span><span style=\"top:-9.0026265em;\"><span class=\"pstrut\" style=\"height:3.751216em;\"><\/span><span class=\"mord\"><\/span><\/span><span style=\"top:-6.558518500000002em;\"><span class=\"pstrut\" style=\"height:3.751216em;\"><\/span><span class=\"mord\"><\/span><\/span><span style=\"top:-3.8955185000000006em;\"><span class=\"pstrut\" style=\"height:3.751216em;\"><\/span><span class=\"mord\"><\/span><\/span><span style=\"top:-0.9083025000000007em;\"><span class=\"pstrut\" style=\"height:3.751216em;\"><\/span><span class=\"mord\"><\/span><\/span><span style=\"top:2.0699134999999984em;\"><span class=\"pstrut\" style=\"height:3.751216em;\"><\/span><span class=\"mord\"><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:7.0914104999999985em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"col-align-l\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:7.5914105em;\"><span style=\"top:-10.5026265em;\"><span class=\"pstrut\" style=\"height:3.751216em;\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mopen\">{<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&lt;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mord\">&#x2223;<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.22222em;\">Y<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mclose\">}<\/span><\/span><\/span><span style=\"top:-9.0026265em;\"><span class=\"pstrut\" style=\"height:3.751216em;\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.69444em;\"><span style=\"top:-2.382892em;margin-left:0em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">&#x3F5;<\/span><span class=\"mrel mtight\">&#x2192;<\/span><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span><span class=\"mop\">lim<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.717108em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mopen\">{<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x2264;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x2223;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&lt;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.22222em;\">Y<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x2264;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mord mathnormal\">&#x3F5;<\/span><span class=\"mclose\">}<\/span><\/span><\/span><span style=\"top:-6.558518500000002em;\"><span class=\"pstrut\" style=\"height:3.751216em;\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.69444em;\"><span style=\"top:-2.382892em;margin-left:0em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">&#x3F5;<\/span><span class=\"mrel mtight\">&#x2192;<\/span><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span><span class=\"mop\">lim<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.717108em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.427em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mopen\">{<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&lt;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.22222em;\">Y<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x2264;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mord mathnormal\">&#x3F5;<\/span><span class=\"mclose\">}<\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mopen\">{<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x2264;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&lt;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.22222em;\">Y<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x2264;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mord mathnormal\">&#x3F5;<\/span><span class=\"mclose\">}<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.936em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><span style=\"top:-3.8955185000000006em;\"><span class=\"pstrut\" style=\"height:3.751216em;\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.69444em;\"><span style=\"top:-2.342135em;margin-left:0em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">&#x3B5;<\/span><span class=\"mrel mtight\">&#x2192;<\/span><span class=\"mord mtight\"><span class=\"mord mtight\">0<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7026642857142857em;\"><span style=\"top:-2.786em;margin-right:0.07142857142857144em;\"><span class=\"pstrut\" style=\"height:2.5em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">+<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span><span class=\"mop\">lim<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.757865em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.427em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.32833099999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mord mathnormal\">&#x3B5;<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.32833099999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mclose\">)<\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">F<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mord mathnormal\">&#x3B5;<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">F<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.936em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><span style=\"top:-0.9083025000000007em;\"><span class=\"pstrut\" style=\"height:3.751216em;\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.7512159999999999em;\"><span style=\"top:-2.229892em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8801079999999999em;\"><span style=\"top:-2.6550000000000002em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\" style=\"margin-right:0.05556em;\">&#x2202;<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right:0.03588em;\">y<\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.394em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\" style=\"margin-right:0.05556em;\">&#x2202;<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.481108em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.32833099999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mclose\">)<\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.871108em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8801079999999999em;\"><span style=\"top:-2.6550000000000002em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\" style=\"margin-right:0.05556em;\">&#x2202;<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right:0.03588em;\">y<\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.394em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\" style=\"margin-right:0.05556em;\">&#x2202;<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.481108em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">F<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.2512159999999999em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><span style=\"top:2.0699134999999984em;\"><span class=\"pstrut\" style=\"height:3.751216em;\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol large-op\" style=\"margin-right:0.44445em;position:relative;top:-0.0011249999999999316em;\">&#x222B;<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.414292em;\"><span style=\"top:-1.7880500000000001em;margin-left:-0.44445em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">&#x2212;<\/span><span class=\"mord mtight\">&#x221E;<\/span><\/span><\/span><\/span><span style=\"top:-3.8129000000000004em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.970281em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.427em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.32833099999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mclose\">)<\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.936em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mord mathnormal\">u<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:7.0914104999999985em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace newline\"><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1.1052em;vertical-align:-0.3551999999999999em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.34480000000000005em;\"><span style=\"top:-2.5198em;margin-left:-0.10764em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mord mtight\">&#x2223;<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right:0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3551999999999999em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mord\">&#x2223;<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:2.363em;vertical-align:-0.936em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.427em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.32833099999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.22222em;\">Y<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mclose\">)<\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.936em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h3 class=\"mume-header\" id=\"%E5%87%A0%E4%BD%95%E4%B8%8A%E7%9A%84%E8%A7%A3%E9%87%8A\">&#x51E0;&#x4F55;&#x4E0A;&#x7684;&#x89E3;&#x91CA;<\/h3>\n\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>f<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo separator=\"true\">,<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><msub><mi>f<\/mi><mrow><mi>X<\/mi><mi mathvariant=\"normal\">&#x2223;<\/mi><mi>Y<\/mi><\/mrow><\/msub><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mi mathvariant=\"normal\">&#x2223;<\/mi><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><msub><mi>f<\/mi><mi>Y<\/mi><\/msub><mo stretchy=\"false\">(<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">f(x,y)=f_{X|Y}(x|y)f_Y(y)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1.1052em;vertical-align:-0.3551999999999999em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.34480000000000005em;\"><span style=\"top:-2.5198em;margin-left:-0.10764em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mord mtight\">&#x2223;<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right:0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3551999999999999em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mord\">&#x2223;<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mclose\">)<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.32833099999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.22222em;\">Y<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><br>\n&#x53EF;&#x4EE5;&#x770B;&#x4F5C;&#x662F;&#x5229;&#x7528;&#x8FB9;&#x7F18;&#x5206;&#x5E03;&#x5BF9;&#x6761;&#x4EF6;&#x5206;&#x5E03;&#x8FDB;&#x884C;&#x4E86;&#x8C03;&#x5236;<\/p>\n<p><img src=\"https:\/\/i0.wp.com\/www.lazybirds.top\/wp-content\/uploads\/2021\/11\/mmexport1636202176631.jpg?w=840&#038;ssl=1\" alt data-recalc-dims=\"1\"><\/p>\n<h2 class=\"mume-header\" id=\"%E4%BA%8C%E7%BB%B4%E9%9A%8F%E6%9C%BA%E5%8F%98%E9%87%8F%E5%87%BD%E6%95%B0%E7%9A%84%E5%88%86%E5%B8%83\">&#x4E8C;&#x7EF4;&#x968F;&#x673A;&#x53D8;&#x91CF;&#x51FD;&#x6570;&#x7684;&#x5206;&#x5E03;<\/h2>\n\n<h3 class=\"mume-header\" id=\"zxy\">Z=X+Y<\/h3>\n\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msub><mi>f<\/mi><mi>Z<\/mi><\/msub><mo stretchy=\"false\">(<\/mo><mi>z<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><msubsup><mo>&#x222B;<\/mo><mrow><mo>&#x2212;<\/mo><mi mathvariant=\"normal\">&#x221E;<\/mi><\/mrow><mi mathvariant=\"normal\">&#x221E;<\/mi><\/msubsup><mi>f<\/mi><mo stretchy=\"false\">(<\/mo><mi>z<\/mi><mo>&#x2212;<\/mo><mi>y<\/mi><mo separator=\"true\">,<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><mi>d<\/mi><mi>y<\/mi><mo>=<\/mo><msubsup><mo>&#x222B;<\/mo><mrow><mo>&#x2212;<\/mo><mi mathvariant=\"normal\">&#x221E;<\/mi><\/mrow><mi mathvariant=\"normal\">&#x221E;<\/mi><\/msubsup><mi>f<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo separator=\"true\">,<\/mo><mi>z<\/mi><mo>&#x2212;<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><mi>d<\/mi><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">f_{Z}(z)=\\int_{-\\infty}^{\\infty} f(z-y, y) d y=\\int_{-\\infty}^{\\infty} f(x, z-x) d x<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.32833099999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.07153em;\">Z<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.04398em;\">z<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:2.384573em;vertical-align:-0.970281em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol large-op\" style=\"margin-right:0.44445em;position:relative;top:-0.0011249999999999316em;\">&#x222B;<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.414292em;\"><span style=\"top:-1.7880500000000001em;margin-left:-0.44445em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">&#x2212;<\/span><span class=\"mord mtight\">&#x221E;<\/span><\/span><\/span><\/span><span style=\"top:-3.8129000000000004em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">&#x221E;<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.970281em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.04398em;\">z<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:2.384573em;vertical-align:-0.970281em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol large-op\" style=\"margin-right:0.44445em;position:relative;top:-0.0011249999999999316em;\">&#x222B;<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.414292em;\"><span style=\"top:-1.7880500000000001em;margin-left:-0.44445em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">&#x2212;<\/span><span class=\"mord mtight\">&#x221E;<\/span><\/span><\/span><\/span><span style=\"top:-3.8129000000000004em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">&#x221E;<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.970281em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.04398em;\">z<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span><br>\n&#x5F53;X&#xFF0C;Y&#x76F8;&#x4E92;&#x72EC;&#x7ACB;&#x65F6;&#xFF0C;<br>\n<span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msub><mi>f<\/mi><mi>Z<\/mi><\/msub><mo>=<\/mo><msub><mi>f<\/mi><mi>X<\/mi><\/msub><mo>&#x2217;<\/mo><msub><mi>f<\/mi><mi>Y<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">f_Z=f_X*f_Y<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.8888799999999999em;vertical-align:-0.19444em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.32833099999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.07153em;\">Z<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.8888799999999999em;vertical-align:-0.19444em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.32833099999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.07847em;\">X<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">&#x2217;<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.8888799999999999em;vertical-align:-0.19444em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.32833099999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.22222em;\">Y<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><br>\n&#x63A8;&#x8BBA;&#xFF1A;&#x6709;&#x9650;&#x4E2A;&#x76F8;&#x4E92;&#x72EC;&#x7ACB;&#x7684;&#x6B63;&#x6001;&#x968F;&#x673A;&#x53D8;&#x91CF;&#x7684;&#x7EBF;&#x6027;&#x7EC4;&#x5408;&#x4ECD;&#x7136;&#x670D;&#x4ECE;&#x6B63;&#x6001;&#x5206;&#x5E03;<br>\n&#x82E5; <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>X<\/mi><mi>i<\/mi><\/msub><mo>&#x223C;<\/mo><mi>N<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi>&#x3BC;<\/mi><mi>i<\/mi><\/msub><mo separator=\"true\">,<\/mo><msubsup><mi>&#x3C3;<\/mi><mi>i<\/mi><mn>2<\/mn><\/msubsup><mo fence=\"true\">)<\/mo><\/mrow><mo stretchy=\"false\">(<\/mo><mi>i<\/mi><mo>=<\/mo><mn>1<\/mn><mo separator=\"true\">,<\/mo><mn>2<\/mn><mo separator=\"true\">,<\/mo><mo>&#x2026;<\/mo><mo separator=\"true\">,<\/mo><mi>n<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">X_{i} \\sim N\\left(\\mu_{i}, \\sigma_{i}^{2}\\right)(i=1,2, \\ldots, n)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.83333em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.31166399999999994em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x223C;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1.20001em;vertical-align:-0.35001em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.10903em;\">N<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">&#x3BC;<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.31166399999999994em;\"><span style=\"top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">&#x3C3;<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8141079999999999em;\"><span style=\"top:-2.441336em;margin-left:-0.03588em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.258664em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">i<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord\">2<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"minner\">&#x2026;<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span> &#xFF0C; &#x4E14;&#x76F8;&#x4E92;&#x72EC;&#x7ACB;&#xFF0C; <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>Z<\/mi><mo>=<\/mo><msubsup><mo>&#x2211;<\/mo><mrow><mi>i<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mi>n<\/mi><\/msubsup><msub><mi>X<\/mi><mi>i<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">Z=\\sum_{i=1}^{n} X_{i}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.68333em;vertical-align:0em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07153em;\">Z<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1.104002em;vertical-align:-0.29971000000000003em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position:relative;top:-0.0000050000000000050004em;\">&#x2211;<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.804292em;\"><span style=\"top:-2.40029em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span style=\"top:-3.2029em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.29971000000000003em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.31166399999999994em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> &#xFF0C;<br>\n&#x5219; <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>Z<\/mi><mo>&#x223C;<\/mo><mi>N<\/mi><mrow><mo fence=\"true\">(<\/mo><msubsup><mo>&#x2211;<\/mo><mrow><mi>i<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mi>n<\/mi><\/msubsup><msub><mi>&#x3BC;<\/mi><mi>i<\/mi><\/msub><mo separator=\"true\">,<\/mo><msubsup><mo>&#x2211;<\/mo><mrow><mi>i<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mi>n<\/mi><\/msubsup><msubsup><mi>&#x3C3;<\/mi><mi>i<\/mi><mn>2<\/mn><\/msubsup><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">Z \\sim N\\left(\\sum_{i=1}^{n} \\mu_{i}, \\sum_{i=1}^{n} \\sigma_{i}^{2}\\right)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.68333em;vertical-align:0em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07153em;\">Z<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x223C;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1.20001em;vertical-align:-0.35001em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.10903em;\">N<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position:relative;top:-0.0000050000000000050004em;\">&#x2211;<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.804292em;\"><span style=\"top:-2.40029em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span style=\"top:-3.2029em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.29971000000000003em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">&#x3BC;<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.31166399999999994em;\"><span style=\"top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position:relative;top:-0.0000050000000000050004em;\">&#x2211;<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.804292em;\"><span style=\"top:-2.40029em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span style=\"top:-3.2029em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.29971000000000003em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">&#x3C3;<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8141079999999999em;\"><span style=\"top:-2.441336em;margin-left:-0.03588em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.258664em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h3 class=\"mume-header\" id=\"zyx\">Z=Y\/X<\/h3>\n\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msub><mi>f<\/mi><mrow><mi>Y<\/mi><mi mathvariant=\"normal\">\/<\/mi><mi>X<\/mi><\/mrow><\/msub><mo stretchy=\"false\">(<\/mo><mi>z<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><msubsup><mo>&#x222B;<\/mo><mrow><mo>&#x2212;<\/mo><mi mathvariant=\"normal\">&#x221E;<\/mi><\/mrow><mi mathvariant=\"normal\">&#x221E;<\/mi><\/msubsup><mi mathvariant=\"normal\">&#x2223;<\/mi><mi>x<\/mi><mi mathvariant=\"normal\">&#x2223;<\/mi><mi>f<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo separator=\"true\">,<\/mo><mi>x<\/mi><mi>z<\/mi><mo stretchy=\"false\">)<\/mo><mi>d<\/mi><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">f_{Y \/ X}(z)=\\int_{-\\infty}^{\\infty}|x| f(x, x z) d x<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1.1052em;vertical-align:-0.3551999999999999em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.34480000000000005em;\"><span style=\"top:-2.5198em;margin-left:-0.10764em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.22222em;\">Y<\/span><span class=\"mord mtight\">\/<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right:0.07847em;\">X<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3551999999999999em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.04398em;\">z<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:2.384573em;vertical-align:-0.970281em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol large-op\" style=\"margin-right:0.44445em;position:relative;top:-0.0011249999999999316em;\">&#x222B;<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.414292em;\"><span style=\"top:-1.7880500000000001em;margin-left:-0.44445em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">&#x2212;<\/span><span class=\"mord mtight\">&#x221E;<\/span><\/span><\/span><\/span><span style=\"top:-3.8129000000000004em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">&#x221E;<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.970281em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord\">&#x2223;<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mord\">&#x2223;<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.04398em;\">z<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span><\/p>\n<h3 class=\"mume-header\" id=\"zxy-1\">Z=XY<\/h3>\n\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msub><mi>f<\/mi><mrow><mi>X<\/mi><mi>Y<\/mi><\/mrow><\/msub><mo stretchy=\"false\">(<\/mo><mi>z<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><msubsup><mo>&#x222B;<\/mo><mrow><mo>&#x2212;<\/mo><mi mathvariant=\"normal\">&#x221E;<\/mi><\/mrow><mi mathvariant=\"normal\">&#x221E;<\/mi><\/msubsup><mrow><mo fence=\"true\">&#x2223;<\/mo><mfrac><mn>1<\/mn><mi>x<\/mi><\/mfrac><mo fence=\"true\">&#x2223;<\/mo><\/mrow><mi>f<\/mi><mrow><mo fence=\"true\">(<\/mo><mi>x<\/mi><mo separator=\"true\">,<\/mo><mfrac><mi>z<\/mi><mi>x<\/mi><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><mi>d<\/mi><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">f_{X Y}(z)=\\int_{-\\infty}^{\\infty}\\left|\\frac{1}{x}\\right| f\\left(x, \\frac{z}{x}\\right) d x<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.32833099999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right:0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.04398em;\">z<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:2.4322809999999997em;vertical-align:-0.970281em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol large-op\" style=\"margin-right:0.44445em;position:relative;top:-0.0011249999999999316em;\">&#x222B;<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.414292em;\"><span style=\"top:-1.7880500000000001em;margin-left:-0.44445em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">&#x2212;<\/span><span class=\"mord mtight\">&#x221E;<\/span><\/span><\/span><\/span><span style=\"top:-3.8129000000000004em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">&#x221E;<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.970281em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"minner\"><span class=\"mopen\"><span class=\"delimsizing mult\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.462em;\"><span style=\"top:-2.266em;\"><span class=\"pstrut\" style=\"height:3.21602em;\"><\/span><span class=\"delimsizinginner delim-size1\"><span>&#x2223;<\/span><\/span><\/span><span style=\"top:-2.864em;\"><span class=\"pstrut\" style=\"height:3.21602em;\"><\/span><span style=\"height:1.2160199999999999em;width:0.333em;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"0.333em\" height=\"1.2160199999999999em\" style=\"width:0.333em\" viewBox=\"0 0 333 1216\" preserveAspectRatio=\"xMinYMin\"><path d=\"M145 0 H188 V1216 H145z M145 0 H188 V1216 H145z\"\/><\/svg><\/span><\/span><span style=\"top:-4.07202em;\"><span class=\"pstrut\" style=\"height:3.21602em;\"><\/span><span class=\"delimsizinginner delim-size1\"><span>&#x2223;<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9500199999999999em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.32144em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.686em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mclose\"><span class=\"delimsizing mult\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.462em;\"><span style=\"top:-2.266em;\"><span class=\"pstrut\" style=\"height:3.21602em;\"><\/span><span class=\"delimsizinginner delim-size1\"><span>&#x2223;<\/span><\/span><\/span><span style=\"top:-2.864em;\"><span class=\"pstrut\" style=\"height:3.21602em;\"><\/span><span style=\"height:1.2160199999999999em;width:0.333em;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"0.333em\" height=\"1.2160199999999999em\" style=\"width:0.333em\" viewBox=\"0 0 333 1216\" preserveAspectRatio=\"xMinYMin\"><path d=\"M145 0 H188 V1216 H145z M145 0 H188 V1216 H145z\"\/><\/svg><\/span><\/span><span style=\"top:-4.07202em;\"><span class=\"pstrut\" style=\"height:3.21602em;\"><\/span><span class=\"delimsizinginner delim-size1\"><span>&#x2223;<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9500199999999999em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\"><span class=\"delimsizing size2\">(<\/span><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.10756em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.04398em;\">z<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.686em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\"><span class=\"delimsizing size2\">)<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span><\/p>\n<h3 class=\"mume-header\" id=\"maxxy\">max{X,Y}<\/h3>\n\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msub><mi>F<\/mi><mrow><mi>max<\/mi><mo>&#x2061;<\/mo><mo stretchy=\"false\">(<\/mo><mi>X<\/mi><mo separator=\"true\">,<\/mo><mi>Y<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/msub><mo stretchy=\"false\">(<\/mo><mi>z<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><msub><mi>F<\/mi><mi>X<\/mi><\/msub><mo stretchy=\"false\">(<\/mo><mi>z<\/mi><mo stretchy=\"false\">)<\/mo><msub><mi>F<\/mi><mi>Y<\/mi><\/msub><mo stretchy=\"false\">(<\/mo><mi>z<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">F_{\\max (X, Y)}(z)=F_{X}(z) F_{Y}(z)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1.1052em;vertical-align:-0.3551999999999999em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.34480000000000005em;\"><span style=\"top:-2.5198em;margin-left:-0.13889em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mop mtight\"><span class=\"mtight\">m<\/span><span class=\"mtight\">a<\/span><span class=\"mtight\">x<\/span><\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right:0.22222em;\">Y<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3551999999999999em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.04398em;\">z<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.32833099999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.07847em;\">X<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.04398em;\">z<\/span><span class=\"mclose\">)<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.32833099999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.04398em;\">z<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/p>\n<h3 class=\"mume-header\" id=\"minxy\">min{X,Y}<\/h3>\n\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msub><mi>F<\/mi><mrow><mi>min<\/mi><mo>&#x2061;<\/mo><mo stretchy=\"false\">(<\/mo><mi>X<\/mi><mo separator=\"true\">,<\/mo><mi>Y<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/msub><mo stretchy=\"false\">(<\/mo><mi>z<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>1<\/mn><mo>&#x2212;<\/mo><mrow><mo fence=\"true\">[<\/mo><mn>1<\/mn><mo>&#x2212;<\/mo><msub><mi>F<\/mi><mi>X<\/mi><\/msub><mo stretchy=\"false\">(<\/mo><mi>z<\/mi><mo stretchy=\"false\">)<\/mo><mo fence=\"true\">]<\/mo><\/mrow><mrow><mo fence=\"true\">[<\/mo><mn>1<\/mn><mo>&#x2212;<\/mo><msub><mi>F<\/mi><mi>Y<\/mi><\/msub><mo stretchy=\"false\">(<\/mo><mi>z<\/mi><mo stretchy=\"false\">)<\/mo><mo fence=\"true\">]<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">F_{\\min (X, Y)}(z)=1-\\left[1-F_{X}(z)\\right]\\left[1-F_{Y}(z)\\right]<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1.1052em;vertical-align:-0.3551999999999999em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.34480000000000005em;\"><span style=\"top:-2.5198em;margin-left:-0.13889em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mop mtight\"><span class=\"mtight\">m<\/span><span class=\"mtight\">i<\/span><span class=\"mtight\">n<\/span><\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right:0.22222em;\">Y<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3551999999999999em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.04398em;\">z<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.72777em;vertical-align:-0.08333em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">[<\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.32833099999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.07847em;\">X<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.04398em;\">z<\/span><span class=\"mclose\">)<\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">]<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">[<\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.32833099999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.04398em;\">z<\/span><span class=\"mclose\">)<\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">]<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h1 class=\"mume-header\" id=\"%E9%9A%8F%E6%9C%BA%E5%8F%98%E9%87%8F%E7%9A%84%E6%95%B0%E5%AD%97%E7%89%B9%E5%BE%81\">&#x968F;&#x673A;&#x53D8;&#x91CF;&#x7684;&#x6570;&#x5B57;&#x7279;&#x5F81;<\/h1>\n\n<h2 class=\"mume-header\" id=\"%E6%9C%9F%E6%9C%9B\">&#x671F;&#x671B;<\/h2>\n\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>E<\/mi><mo stretchy=\"false\">(<\/mo><mi>X<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mo>&#x222B;<\/mo><mi>x<\/mi><mtext>&#xA0;<\/mtext><mi mathvariant=\"bold\">d<\/mi><mi>F<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">E(X)=\\int x~\\mathbf{d}F(x)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.05764em;\">E<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:2.22225em;vertical-align:-0.86225em;\"><\/span><span class=\"mop op-symbol large-op\" style=\"margin-right:0.44445em;position:relative;top:-0.0011249999999999316em;\">&#x222B;<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace nobreak\">&#xA0;<\/span><span class=\"mord mathbf\">d<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">F<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/p>\n<h2 class=\"mume-header\" id=\"%E6%96%B9%E5%B7%AE\">&#x65B9;&#x5DEE;<\/h2>\n\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>D<\/mi><mo stretchy=\"false\">(<\/mo><mi>X<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mo>&#x222B;<\/mo><mo stretchy=\"false\">[<\/mo><mi>x<\/mi><mo>&#x2212;<\/mo><mi>E<\/mi><mo stretchy=\"false\">(<\/mo><mi>X<\/mi><mo stretchy=\"false\">)<\/mo><msup><mo stretchy=\"false\">]<\/mo><mn>2<\/mn><\/msup><mtext>&#xA0;<\/mtext><mi mathvariant=\"bold\">d<\/mi><mi>F<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">D(X)=\\int [x-E(X)]^2~\\mathbf{d}F(x)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.02778em;\">D<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:2.22225em;vertical-align:-0.86225em;\"><\/span><span class=\"mop op-symbol large-op\" style=\"margin-right:0.44445em;position:relative;top:-0.0011249999999999316em;\">&#x222B;<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1.1141079999999999em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.05764em;\">E<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mclose\">)<\/span><span class=\"mclose\"><span class=\"mclose\">]<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8641079999999999em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace nobreak\">&#xA0;<\/span><span class=\"mord mathbf\">d<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">F<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/p>\n<h2 class=\"mume-header\" id=\"%E6%A0%B7%E6%9C%AC%E5%9D%87%E5%80%BC\">&#x6837;&#x672C;&#x5747;&#x503C;<\/h2>\n\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msub><mover accent=\"true\"><mi>X<\/mi><mo>&#x2C9;<\/mo><\/mover><mi>n<\/mi><\/msub><mo>=<\/mo><mfrac><mn>1<\/mn><mi>n<\/mi><\/mfrac><munderover><mo>&#x2211;<\/mo><mrow><mi>i<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mi>n<\/mi><\/munderover><msub><mi>X<\/mi><mi>i<\/mi><\/msub><mspace linebreak=\"newline\"><\/mspace><mi>E<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mover accent=\"true\"><mi>X<\/mi><mo>&#x2C9;<\/mo><\/mover><mi>n<\/mi><\/msub><mo fence=\"true\">)<\/mo><\/mrow><mo>=<\/mo><mi>&#x3BC;<\/mi><mo separator=\"true\">,<\/mo><mspace width=\"1em\"><\/mspace><mi>D<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mover accent=\"true\"><mi>X<\/mi><mo>&#x2C9;<\/mo><\/mover><mi>n<\/mi><\/msub><mo fence=\"true\">)<\/mo><\/mrow><mo>=<\/mo><mfrac><msup><mi>&#x3C3;<\/mi><mn>2<\/mn><\/msup><mi>n<\/mi><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\bar{X}_{n}=\\frac{1}{n} \\sum_{i=1}^{n} X_{i} \\\\\nE\\left(\\bar{X}_{n}\\right)=\\mu, \\quad D\\left(\\bar{X}_{n}\\right)=\\frac{\\sigma^{2}}{n}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.9701099999999999em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8201099999999999em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><\/span><span style=\"top:-3.25233em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.16666em;\"><span class=\"mord\">&#x2C9;<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.151392em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:2.929066em;vertical-align:-1.277669em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.32144em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.686em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.6513970000000002em;\"><span style=\"top:-1.872331em;margin-left:0em;\"><span class=\"pstrut\" style=\"height:3.05em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span style=\"top:-3.050005em;\"><span class=\"pstrut\" style=\"height:3.05em;\"><\/span><span><span class=\"mop op-symbol large-op\">&#x2211;<\/span><\/span><\/span><span style=\"top:-4.3000050000000005em;margin-left:0em;\"><span class=\"pstrut\" style=\"height:3.05em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.277669em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.31166399999999994em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace newline\"><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1.20001em;vertical-align:-0.35001em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.05764em;\">E<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8201099999999999em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><\/span><span style=\"top:-3.25233em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.16666em;\"><span class=\"mord\">&#x2C9;<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.151392em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1.20001em;vertical-align:-0.35001em;\"><\/span><span class=\"mord mathnormal\">&#x3BC;<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:1em;\"><\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.02778em;\">D<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8201099999999999em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><\/span><span style=\"top:-3.25233em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.16666em;\"><span class=\"mord\">&#x2C9;<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.151392em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:2.177108em;vertical-align:-0.686em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.491108em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">&#x3C3;<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8141079999999999em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.686em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h2 class=\"mume-header\" id=\"%E6%A0%B7%E6%9C%AC%E6%96%B9%E5%B7%AE\">&#x6837;&#x672C;&#x65B9;&#x5DEE;<\/h2>\n\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msubsup><mi>S<\/mi><mi>n<\/mi><mn>2<\/mn><\/msubsup><mo>=<\/mo><mfrac><mn>1<\/mn><mrow><mi>n<\/mi><mo>&#x2212;<\/mo><mn>1<\/mn><\/mrow><\/mfrac><munderover><mo>&#x2211;<\/mo><mrow><mi>i<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mi>n<\/mi><\/munderover><msup><mrow><mo fence=\"true\">(<\/mo><msub><mi>X<\/mi><mi>i<\/mi><\/msub><mo>&#x2212;<\/mo><msub><mover accent=\"true\"><mi>X<\/mi><mo>&#x2C9;<\/mo><\/mover><mi>n<\/mi><\/msub><mo fence=\"true\">)<\/mo><\/mrow><mn>2<\/mn><\/msup><mspace linebreak=\"newline\"><\/mspace><mi>E<\/mi><mrow><mo fence=\"true\">(<\/mo><msubsup><mi>S<\/mi><mi>n<\/mi><mn>2<\/mn><\/msubsup><mo fence=\"true\">)<\/mo><\/mrow><mo>=<\/mo><msup><mi>&#x3C3;<\/mi><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">S_{n}^{2}=\\frac{1}{n-1} \\sum_{i=1}^{n}\\left(X_{i}-\\bar{X}_{n}\\right)^{2}\\\\\nE\\left(S_{n}^{2}\\right)=\\sigma^{2}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1.1111079999999998em;vertical-align:-0.247em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.05764em;\">S<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8641079999999999em;\"><span style=\"top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.247em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:2.929066em;vertical-align:-1.277669em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.32144em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7693300000000001em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.6513970000000002em;\"><span style=\"top:-1.872331em;margin-left:0em;\"><span class=\"pstrut\" style=\"height:3.05em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span style=\"top:-3.050005em;\"><span class=\"pstrut\" style=\"height:3.05em;\"><\/span><span><span class=\"mop op-symbol large-op\">&#x2211;<\/span><\/span><\/span><span style=\"top:-4.3000050000000005em;margin-left:0em;\"><span class=\"pstrut\" style=\"height:3.05em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.277669em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"minner\"><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.31166399999999994em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8201099999999999em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><\/span><span style=\"top:-3.25233em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.16666em;\"><span class=\"mord\">&#x2C9;<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.151392em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.054008em;\"><span style=\"top:-3.3029em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace newline\"><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1.2141179999999998em;vertical-align:-0.35001em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.05764em;\">E<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.05764em;\">S<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8641079999999999em;\"><span style=\"top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.247em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.8641079999999999em;vertical-align:0em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">&#x3C3;<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8641079999999999em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h2 class=\"mume-header\" id=\"chebyshev-%E4%B8%8D%E7%AD%89%E5%BC%8F\">Chebyshev &#x4E0D;&#x7B49;&#x5F0F;<\/h2>\n\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mtable rowspacing=\"0.2500em\" columnalign=\"center\" columnspacing=\"0em\"><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mi>P<\/mi><mo stretchy=\"false\">{<\/mo><mi mathvariant=\"normal\">&#x2223;<\/mi><mi>X<\/mi><mo>&#x2212;<\/mo><mi>&#x3BC;<\/mi><mi mathvariant=\"normal\">&#x2223;<\/mi><mo>&#x2265;<\/mo><mi>&#x3F5;<\/mi><mo stretchy=\"false\">}<\/mo><mo>&#x2264;<\/mo><mfrac><msup><mi>&#x3C3;<\/mi><mn>2<\/mn><\/msup><msup><mi>&#x3F5;<\/mi><mn>2<\/mn><\/msup><\/mfrac><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mo fence=\"true\">(<\/mo><mtext>&#xA0;&#x7B49;&#x4EF7;&#x5730;:&#xA0;<\/mtext><mi>P<\/mi><mo stretchy=\"false\">{<\/mo><mi mathvariant=\"normal\">&#x2223;<\/mi><mi>X<\/mi><mo>&#x2212;<\/mo><mi>&#x3BC;<\/mi><mi mathvariant=\"normal\">&#x2223;<\/mi><mo>&lt;<\/mo><mi>&#x3F5;<\/mi><mo stretchy=\"false\">}<\/mo><mo>&#x2265;<\/mo><mn>1<\/mn><mo>&#x2212;<\/mo><mfrac><msup><mi>&#x3C3;<\/mi><mn>2<\/mn><\/msup><msup><mi>&#x3F5;<\/mi><mn>2<\/mn><\/msup><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><\/mstyle><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">\\begin{gathered}\nP\\{|X-\\mu| \\geq \\epsilon\\} \\leq \\frac{\\sigma^{2}}{\\epsilon^{2}} \\\\\n\\left(\\text { &#x7B49;&#x4EF7;&#x5730;: } P\\{|X-\\mu|&lt;\\epsilon\\} \\geq 1-\\frac{\\sigma^{2}}{\\epsilon^{2}}\\right)\n\\end{gathered}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:5.218246000000001em;vertical-align:-2.3591230000000003em;\"><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:2.8591230000000003em;\"><span style=\"top:-4.859123em;\"><span class=\"pstrut\" style=\"height:3.491108em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mopen\">{<\/span><span class=\"mord\">&#x2223;<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mord mathnormal\">&#x3BC;<\/span><span class=\"mord\">&#x2223;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x2265;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\">&#x3F5;<\/span><span class=\"mclose\">}<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x2264;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.491108em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\">&#x3F5;<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.740108em;\"><span style=\"top:-2.9890000000000003em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">&#x3C3;<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8141079999999999em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.686em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><span style=\"top:-2.382015em;\"><span class=\"pstrut\" style=\"height:3.491108em;\"><\/span><span class=\"mord\"><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\"><span class=\"delimsizing size3\">(<\/span><\/span><span class=\"mord text\"><span class=\"mord\">&#xA0;<\/span><span class=\"mord cjk_fallback\">&#x7B49;&#x4EF7;&#x5730;<\/span><span class=\"mord\">:&#xA0;<\/span><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mopen\">{<\/span><span class=\"mord\">&#x2223;<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mord mathnormal\">&#x3BC;<\/span><span class=\"mord\">&#x2223;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&lt;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\">&#x3F5;<\/span><span class=\"mclose\">}<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x2265;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.491108em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\">&#x3F5;<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.740108em;\"><span style=\"top:-2.9890000000000003em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">&#x3C3;<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8141079999999999em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.686em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\"><span class=\"delimsizing size3\">)<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:2.3591230000000003em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><br>\n&#x8BC1;&#x660E;&#xFF1A;<br>\n<span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mtable rowspacing=\"0.2500em\" columnalign=\"right left\" columnspacing=\"0em\"><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mi>P<\/mi><mo stretchy=\"false\">{<\/mo><mo>&#x2223;<\/mo><mi>X<\/mi><\/mrow><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mrow><\/mrow><mo>&#x2212;<\/mo><mi>&#x3BC;<\/mi><mo>&#x2223;<\/mo><mo>&#x2265;<\/mo><mi>&#x3F5;<\/mi><mo stretchy=\"false\">}<\/mo><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><\/mrow><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mrow><\/mrow><mo>=<\/mo><msub><mo>&#x222B;<\/mo><mrow><mi mathvariant=\"normal\">&#x2223;<\/mi><mi>x<\/mi><mo>&#x2212;<\/mo><mi>&#x3BC;<\/mi><mi mathvariant=\"normal\">&#x2223;<\/mi><mo>&#x2265;<\/mo><mi>&#x3F5;<\/mi><\/mrow><\/msub><mi>f<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><mi>d<\/mi><mi>x<\/mi><mo>&#x2264;<\/mo><msub><mo>&#x222B;<\/mo><mrow><mi mathvariant=\"normal\">&#x2223;<\/mi><mi>x<\/mi><mo>&#x2212;<\/mo><mi>&#x3BC;<\/mi><mi mathvariant=\"normal\">&#x2223;<\/mi><mo>&#x2265;<\/mo><mi>&#x3F5;<\/mi><\/mrow><\/msub><mfrac><mrow><mi mathvariant=\"normal\">&#x2223;<\/mi><mi>x<\/mi><mo>&#x2212;<\/mo><mi>&#x3BC;<\/mi><msup><mi mathvariant=\"normal\">&#x2223;<\/mi><mn>2<\/mn><\/msup><\/mrow><msup><mi>&#x3F5;<\/mi><mn>2<\/mn><\/msup><\/mfrac><mi>f<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><mi>d<\/mi><mi>x<\/mi><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><\/mrow><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mrow><\/mrow><mo>&#x2264;<\/mo><mfrac><mn>1<\/mn><msup><mi>&#x3F5;<\/mi><mn>2<\/mn><\/msup><\/mfrac><msubsup><mo>&#x222B;<\/mo><mrow><mo>&#x2212;<\/mo><mi mathvariant=\"normal\">&#x221E;<\/mi><\/mrow><mrow><mo>+<\/mo><mi mathvariant=\"normal\">&#x221E;<\/mi><\/mrow><\/msubsup><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo>&#x2212;<\/mo><mi>&#x3BC;<\/mi><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mi>f<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><mi>d<\/mi><mi>x<\/mi><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><\/mrow><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mrow><\/mrow><mo>=<\/mo><mfrac><msup><mi>&#x3C3;<\/mi><mn>2<\/mn><\/msup><msup><mi>&#x3F5;<\/mi><mn>2<\/mn><\/msup><\/mfrac><\/mrow><\/mstyle><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">\\begin{aligned}\nP\\{\\mid X&amp;-\\mu \\mid \\geq \\epsilon\\} \\\\\n&amp;=\\int_{|x-\\mu| \\geq \\epsilon} f(x) d x \\leq \\int_{|x-\\mu| \\geq \\epsilon} \\frac{|x-\\mu|^{2}}{\\epsilon^{2}} f(x) d x \\\\\n&amp; \\leq \\frac{1}{\\epsilon^{2}} \\int_{-\\infty}^{+\\infty}(x-\\mu)^{2} f(x) d x \\\\\n&amp;=\\frac{\\sigma^{2}}{\\epsilon^{2}}\n\\end{aligned}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:9.646678000000001em;vertical-align:-4.573339em;\"><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-r\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:5.073339000000001em;\"><span style=\"top:-7.754570000000001em;\"><span class=\"pstrut\" style=\"height:3.521231em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mopen\">{<\/span><span class=\"mrel\">&#x2223;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><\/span><\/span><span style=\"top:-5.603462em;\"><span class=\"pstrut\" style=\"height:3.521231em;\"><\/span><span class=\"mord\"><\/span><\/span><span style=\"top:-2.6952810000000005em;\"><span class=\"pstrut\" style=\"height:3.521231em;\"><\/span><span class=\"mord\"><\/span><\/span><span style=\"top:0.0661079999999995em;\"><span class=\"pstrut\" style=\"height:3.521231em;\"><\/span><span class=\"mord\"><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:4.573339em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"col-align-l\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:5.073339000000001em;\"><span style=\"top:-7.754570000000001em;\"><span class=\"pstrut\" style=\"height:3.521231em;\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mord mathnormal\">&#x3BC;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x2223;&#x2265;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord mathnormal\">&#x3F5;<\/span><span class=\"mclose\">}<\/span><\/span><\/span><span style=\"top:-5.603462em;\"><span class=\"pstrut\" style=\"height:3.521231em;\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol large-op\" style=\"margin-right:0.44445em;position:relative;top:-0.0011249999999999316em;\">&#x222B;<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:-0.3869499999999999em;\"><span style=\"top:-1.7880500000000004em;margin-left:-0.44445em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">&#x2223;<\/span><span class=\"mord mathnormal mtight\">x<\/span><span class=\"mbin mtight\">&#x2212;<\/span><span class=\"mord mathnormal mtight\">&#x3BC;<\/span><span class=\"mord mtight\">&#x2223;<\/span><span class=\"mrel mtight\">&#x2265;<\/span><span class=\"mord mathnormal mtight\">&#x3F5;<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.0869499999999999em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x2264;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol large-op\" style=\"margin-right:0.44445em;position:relative;top:-0.0011249999999999316em;\">&#x222B;<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:-0.3869499999999999em;\"><span style=\"top:-1.7880500000000004em;margin-left:-0.44445em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">&#x2223;<\/span><span class=\"mord mathnormal mtight\">x<\/span><span class=\"mbin mtight\">&#x2212;<\/span><span class=\"mord mathnormal mtight\">&#x3BC;<\/span><span class=\"mord mtight\">&#x2223;<\/span><span class=\"mrel mtight\">&#x2265;<\/span><span class=\"mord mathnormal mtight\">&#x3F5;<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.0869499999999999em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.491108em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\">&#x3F5;<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.740108em;\"><span style=\"top:-2.9890000000000003em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">&#x2223;<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mord mathnormal\">&#x3BC;<\/span><span class=\"mord\"><span class=\"mord\">&#x2223;<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8141079999999999em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.686em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><span style=\"top:-2.6952810000000005em;\"><span class=\"pstrut\" style=\"height:3.521231em;\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">&#x2264;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.32144em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\">&#x3F5;<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.740108em;\"><span style=\"top:-2.9890000000000003em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.686em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol large-op\" style=\"margin-right:0.44445em;position:relative;top:-0.0011249999999999316em;\">&#x222B;<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.5212310000000002em;\"><span style=\"top:-1.7880500000000001em;margin-left:-0.44445em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">&#x2212;<\/span><span class=\"mord mtight\">&#x221E;<\/span><\/span><\/span><\/span><span style=\"top:-3.8129000000000004em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">+<\/span><span class=\"mord mtight\">&#x221E;<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.970281em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mord mathnormal\">&#x3BC;<\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8641079999999999em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><span style=\"top:0.0661079999999995em;\"><span class=\"pstrut\" style=\"height:3.521231em;\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.491108em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\">&#x3F5;<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.740108em;\"><span style=\"top:-2.9890000000000003em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">&#x3C3;<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8141079999999999em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.686em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:4.573339em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h2 class=\"mume-header\" id=\"%E5%8D%8F%E6%96%B9%E5%B7%AE\">&#x534F;&#x65B9;&#x5DEE;<\/h2>\n\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>C<\/mi><mi>o<\/mi><mi>v<\/mi><mo stretchy=\"false\">(<\/mo><mi>&#x1D44B;<\/mi><mo separator=\"true\">,<\/mo><mi>&#x1D44C;<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mi>&#x1D438;<\/mi><mrow><mo stretchy=\"false\">[<\/mo><mi>&#x1D44B;<\/mi><mo>&#x2212;<\/mo><mi>&#x1D438;<\/mi><mo stretchy=\"false\">(<\/mo><mi>&#x1D44B;<\/mi><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">]<\/mo><mo stretchy=\"false\">[<\/mo><mi>&#x1D44C;<\/mi><mo>&#x2212;<\/mo><mi>&#x1D438;<\/mi><mo stretchy=\"false\">(<\/mo><mi>&#x1D44C;<\/mi><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">]<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">Cov(&#x1D44B;,&#x1D44C;)= &#x1D438;{[&#x1D44B;&#x2212;&#x1D438;(&#x1D44B;)][&#x1D44C;&#x2212;&#x1D438;(&#x1D44C;)]}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07153em;\">C<\/span><span class=\"mord mathnormal\">o<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">v<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.22222em;\">Y<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.05764em;\">E<\/span><span class=\"mord\"><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.05764em;\">E<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mclose\">)]<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.22222em;\">Y<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.05764em;\">E<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.22222em;\">Y<\/span><span class=\"mclose\">)]<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h3 class=\"mume-header\" id=\"%E6%80%A7%E8%B4%A8\">&#x6027;&#x8D28;<\/h3>\n\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>C<\/mi><mi>o<\/mi><mi>v<\/mi><mo stretchy=\"false\">(<\/mo><mi>&#x1D44B;<\/mi><mo separator=\"true\">,<\/mo><mi>&#x1D44C;<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mi>&#x1D438;<\/mi><mo stretchy=\"false\">(<\/mo><mi>&#x1D44B;<\/mi><mi>&#x1D44C;<\/mi><mo stretchy=\"false\">)<\/mo><mo>&#x2212;<\/mo><mi>&#x1D438;<\/mi><mo stretchy=\"false\">(<\/mo><mi>&#x1D44B;<\/mi><mo stretchy=\"false\">)<\/mo><mi>&#x1D438;<\/mi><mo stretchy=\"false\">(<\/mo><mi>&#x1D44C;<\/mi><mo stretchy=\"false\">)<\/mo><mspace linebreak=\"newline\"><\/mspace><mi>D<\/mi><mo stretchy=\"false\">(<\/mo><mi>X<\/mi><mo>+<\/mo><mi>Y<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mi>D<\/mi><mo stretchy=\"false\">(<\/mo><mi>X<\/mi><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mi>D<\/mi><mo stretchy=\"false\">(<\/mo><mi>Y<\/mi><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mn>2<\/mn><mi>C<\/mi><mi>o<\/mi><mi>v<\/mi><mo stretchy=\"false\">(<\/mo><mi>&#x1D44B;<\/mi><mo separator=\"true\">,<\/mo><mi>&#x1D44C;<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">Cov(&#x1D44B;,&#x1D44C;)=&#x1D438;(&#x1D44B;&#x1D44C;)&#x2212;&#x1D438;(&#x1D44B;)&#x1D438;(&#x1D44C;)\\\\\nD(X+Y)=D(X)+D(Y)+2Cov(&#x1D44B;,&#x1D44C;)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07153em;\">C<\/span><span class=\"mord mathnormal\">o<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">v<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.22222em;\">Y<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.05764em;\">E<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.22222em;\">Y<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.05764em;\">E<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.05764em;\">E<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.22222em;\">Y<\/span><span class=\"mclose\">)<\/span><\/span><span class=\"mspace newline\"><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.02778em;\">D<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.22222em;\">Y<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.02778em;\">D<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.02778em;\">D<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.22222em;\">Y<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\">2<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07153em;\">C<\/span><span class=\"mord mathnormal\">o<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">v<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.22222em;\">Y<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/p>\n<h2 class=\"mume-header\" id=\"%E6%A0%87%E5%87%86%E5%8D%8F%E6%96%B9%E5%B7%AE-%E7%9B%B8%E5%85%B3%E7%B3%BB%E6%95%B0\">&#x6807;&#x51C6;&#x534F;&#x65B9;&#x5DEE; \/ &#x76F8;&#x5173;&#x7CFB;&#x6570;<\/h2>\n\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msub><mi>&#x3C1;<\/mi><mrow><mi>X<\/mi><mi>Y<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><mrow><mi mathvariant=\"normal\">Cov<\/mi><mo>&#x2061;<\/mo><mo stretchy=\"false\">(<\/mo><mi>X<\/mi><mo separator=\"true\">,<\/mo><mi>Y<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><mrow><msqrt><mrow><mi>D<\/mi><mo stretchy=\"false\">(<\/mo><mi>X<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/msqrt><msqrt><mrow><mi>D<\/mi><mo stretchy=\"false\">(<\/mo><mi>Y<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/msqrt><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\rho_{X Y}=\\frac{\\operatorname{Cov}(X, Y)}{\\sqrt{D(X)} \\sqrt{D(Y)}}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.625em;vertical-align:-0.19444em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">&#x3C1;<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.32833099999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right:0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:2.557em;vertical-align:-1.13em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.427em;\"><span style=\"top:-2.175em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.935em;\"><span class=\"svg-align\" style=\"top:-3.2em;\"><span class=\"pstrut\" style=\"height:3.2em;\"><\/span><span class=\"mord\" style=\"padding-left:1em;\"><span class=\"mord mathnormal\" style=\"margin-right:0.02778em;\">D<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mclose\">)<\/span><\/span><\/span><span style=\"top:-2.8950000000000005em;\"><span class=\"pstrut\" style=\"height:3.2em;\"><\/span><span class=\"hide-tail\" style=\"min-width:1.02em;height:1.28em;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"400em\" height=\"1.28em\" viewBox=\"0 0 400000 1296\" preserveAspectRatio=\"xMinYMin slice\"><path d=\"M263,681c0.7,0,18,39.7,52,119\nc34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120\nc340,-704.7,510.7,-1060.3,512,-1067\nl0 -0\nc4.7,-7.3,11,-11,19,-11\nH40000v40H1012.3\ns-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232\nc-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1\ns-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26\nc-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z\nM1001 80h400000v40h-400000z\"\/><\/svg><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.30499999999999994em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.935em;\"><span class=\"svg-align\" style=\"top:-3.2em;\"><span class=\"pstrut\" style=\"height:3.2em;\"><\/span><span class=\"mord\" style=\"padding-left:1em;\"><span class=\"mord mathnormal\" style=\"margin-right:0.02778em;\">D<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.22222em;\">Y<\/span><span class=\"mclose\">)<\/span><\/span><\/span><span style=\"top:-2.8950000000000005em;\"><span class=\"pstrut\" style=\"height:3.2em;\"><\/span><span class=\"hide-tail\" style=\"min-width:1.02em;height:1.28em;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"400em\" height=\"1.28em\" viewBox=\"0 0 400000 1296\" preserveAspectRatio=\"xMinYMin slice\"><path d=\"M263,681c0.7,0,18,39.7,52,119\nc34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120\nc340,-704.7,510.7,-1060.3,512,-1067\nl0 -0\nc4.7,-7.3,11,-11,19,-11\nH40000v40H1012.3\ns-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232\nc-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1\ns-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26\nc-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z\nM1001 80h400000v40h-400000z\"\/><\/svg><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.30499999999999994em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mop\"><span class=\"mord mathrm\" style=\"margin-right:0.01389em;\">Cov<\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.22222em;\">Y<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.13em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>&#x6CE8;&#x610F;&#xFF1A;<\/p>\n<p>&#x662F;&#x5426;&#x76F8;&#x5173;&#x53EA;&#x662F;&#x9488;&#x5BF9;&#x7EBF;&#x6027;&#x5173;&#x7CFB;&#x800C;&#x8A00;&#x7684;&#xFF0C;X&#x4E0E;Y&#x76F8;&#x4E92;&#x72EC;&#x7ACB;&#x5219;&#x662F;&#x76F8;&#x5BF9;&#x4E00;&#x822C;&#x5173;&#x7CFB;&#x800C;&#x8A00;&#x7684;<\/p>\n<p>&#x82E5; <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo fence=\"true\">(<\/mo><msub><mi>X<\/mi><mn>1<\/mn><\/msub><mo separator=\"true\">,<\/mo><msub><mi>X<\/mi><mn>2<\/mn><\/msub><mo separator=\"true\">,<\/mo><mo>&#x2026;<\/mo><mo separator=\"true\">,<\/mo><msub><mi>X<\/mi><mi>n<\/mi><\/msub><mo fence=\"true\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\left(X_{1}, X_{2}, \\ldots, X_{n}\\right)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.30110799999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.30110799999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"minner\">&#x2026;<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.151392em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><\/span><\/span><\/span> &#x670D;&#x4ECE;n&#x7EF4;&#x6B63;&#x6001;&#x5206;&#x5E03;&#xFF0C;&#x5219; <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>X<\/mi><mn>1<\/mn><\/msub><mo separator=\"true\">,<\/mo><msub><mi>X<\/mi><mn>2<\/mn><\/msub><mo separator=\"true\">,<\/mo><mo>&#x2026;<\/mo><mo separator=\"true\">,<\/mo><msub><mi>X<\/mi><mi>n<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">X_{1}, X_{2}, \\ldots, X_{n}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.8777699999999999em;vertical-align:-0.19444em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.30110799999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.30110799999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"minner\">&#x2026;<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.151392em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> &#x76F8;&#x4E92;&#x72EC;&#x7ACB; <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo>&#x21D4;<\/mo><msub><mi>X<\/mi><mn>1<\/mn><\/msub><mo separator=\"true\">,<\/mo><msub><mi>X<\/mi><mn>2<\/mn><\/msub><mo separator=\"true\">,<\/mo><mo>&#x2026;<\/mo><mo separator=\"true\">,<\/mo><msub><mi>X<\/mi><mi>n<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">\\Leftrightarrow X_{1}, X_{2}, \\ldots, X_{n}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.36687em;vertical-align:0em;\"><\/span><span class=\"mrel\">&#x21D4;<\/span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.8777699999999999em;vertical-align:-0.19444em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.30110799999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.30110799999999993em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"minner\">&#x2026;<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.151392em;\"><span style=\"top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> &#x4E24;&#x4E24;&#x4E0D;&#x76F8;&#x5173;<\/p>\n<h2 class=\"mume-header\" id=\"%E7%9F%A9\">&#x77E9;<\/h2>\n\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mtable rowspacing=\"0.2500em\" columnalign=\"right left\" columnspacing=\"0em\"><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mi>E<\/mi><mo stretchy=\"false\">(<\/mo><msup><mi>X<\/mi><mi>k<\/mi><\/msup><mo stretchy=\"false\">)<\/mo><mspace width=\"1em\"><\/mspace><\/mrow><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mrow><\/mrow><mi>X<\/mi><mtext>&#x7684;<\/mtext><mi>k<\/mi><mtext>&#x9636;&#x539F;&#x70B9;&#x77E9;<\/mtext><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mi>E<\/mi><mo stretchy=\"false\">{<\/mo><mo stretchy=\"false\">[<\/mo><mi>X<\/mi><mo>&#x2212;<\/mo><mi>E<\/mi><mo stretchy=\"false\">(<\/mo><mi>X<\/mi><mo stretchy=\"false\">)<\/mo><msup><mo stretchy=\"false\">]<\/mo><mi>k<\/mi><\/msup><mo stretchy=\"false\">}<\/mo><mspace width=\"1em\"><\/mspace><\/mrow><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mrow><\/mrow><mi>X<\/mi><mtext>&#x7684;<\/mtext><mi>k<\/mi><mtext>&#x9636;&#x4E2D;&#x5FC3;&#x77E9;<\/mtext><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mi>E<\/mi><mo stretchy=\"false\">(<\/mo><msup><mi>X<\/mi><mi>k<\/mi><\/msup><msup><mi>Y<\/mi><mi>l<\/mi><\/msup><mo stretchy=\"false\">)<\/mo><mspace width=\"1em\"><\/mspace><\/mrow><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mrow><\/mrow><mi>X<\/mi><mtext>&#x548C;<\/mtext><mi>Y<\/mi><mtext>&#x7684;<\/mtext><mi>k<\/mi><mo>+<\/mo><mi>l<\/mi><mtext>&#x9636;&#x6DF7;&#x5408;&#x77E9;<\/mtext><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mi>E<\/mi><mo stretchy=\"false\">{<\/mo><mo stretchy=\"false\">[<\/mo><mi>X<\/mi><mo>&#x2212;<\/mo><mi>E<\/mi><mo stretchy=\"false\">(<\/mo><mi>X<\/mi><mo stretchy=\"false\">)<\/mo><msup><mo stretchy=\"false\">]<\/mo><mi>k<\/mi><\/msup><mo stretchy=\"false\">[<\/mo><mi>Y<\/mi><mo>&#x2212;<\/mo><mi>E<\/mi><mo stretchy=\"false\">(<\/mo><mi>Y<\/mi><mo stretchy=\"false\">)<\/mo><msup><mo stretchy=\"false\">]<\/mo><mi>l<\/mi><\/msup><mo stretchy=\"false\">}<\/mo><mspace width=\"1em\"><\/mspace><\/mrow><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mrow><\/mrow><mi>X<\/mi><mtext>&#x548C;<\/mtext><mi>Y<\/mi><mtext>&#x7684;<\/mtext><mi>k<\/mi><mo>+<\/mo><mi>l<\/mi><mtext>&#x9636;&#x4E2D;&#x5FC3;&#x77E9;<\/mtext><\/mrow><\/mstyle><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">\\begin{align*}\n    E(X^k)\\quad&amp;X&#x7684;k&#x9636;&#x539F;&#x70B9;&#x77E9;\\\\\n    E\\{[X-E(X)]^k\\}\\quad&amp;X&#x7684;k&#x9636;&#x4E2D;&#x5FC3;&#x77E9;\\\\\n    E(X^kY^l)\\quad&amp;X&#x548C;Y&#x7684;k+l&#x9636;&#x6DF7;&#x5408;&#x77E9;\\\\\n    E\\{[X-E(X)]^k[Y-E(Y)]^l\\}\\quad&amp;X&#x548C;Y&#x7684;k+l&#x9636;&#x4E2D;&#x5FC3;&#x77E9;\n\\end{align*}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:6.236432000000001em;vertical-align:-2.8682160000000003em;\"><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-r\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:3.3682160000000003em;\"><span style=\"top:-5.469108em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.05764em;\">E<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8991079999999999em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.03148em;\">k<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:1em;\"><\/span><\/span><\/span><span style=\"top:-3.91em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.05764em;\">E<\/span><span class=\"mopen\">{[<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.05764em;\">E<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mclose\">)<\/span><span class=\"mclose\"><span class=\"mclose\">]<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8991079999999999em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.03148em;\">k<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">}<\/span><span class=\"mspace\" style=\"margin-right:1em;\"><\/span><\/span><\/span><span style=\"top:-2.350892em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.05764em;\">E<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8991079999999999em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.03148em;\">k<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.22222em;\">Y<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8991079999999999em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.01968em;\">l<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:1em;\"><\/span><\/span><\/span><span style=\"top:-0.7917839999999998em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.05764em;\">E<\/span><span class=\"mopen\">{[<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.05764em;\">E<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mclose\">)<\/span><span class=\"mclose\"><span class=\"mclose\">]<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8991079999999999em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.03148em;\">k<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.22222em;\">Y<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.05764em;\">E<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.22222em;\">Y<\/span><span class=\"mclose\">)<\/span><span class=\"mclose\"><span class=\"mclose\">]<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8991079999999999em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.01968em;\">l<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">}<\/span><span class=\"mspace\" style=\"margin-right:1em;\"><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:2.8682160000000003em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"col-align-l\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:3.3682160000000003em;\"><span style=\"top:-5.469108em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mord cjk_fallback\">&#x7684;<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03148em;\">k<\/span><span class=\"mord cjk_fallback\">&#x9636;&#x539F;&#x70B9;&#x77E9;<\/span><\/span><\/span><span style=\"top:-3.91em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mord cjk_fallback\">&#x7684;<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03148em;\">k<\/span><span class=\"mord cjk_fallback\">&#x9636;&#x4E2D;&#x5FC3;&#x77E9;<\/span><\/span><\/span><span style=\"top:-2.350892em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mord cjk_fallback\">&#x548C;<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.22222em;\">Y<\/span><span class=\"mord cjk_fallback\">&#x7684;<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03148em;\">k<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.01968em;\">l<\/span><span class=\"mord cjk_fallback\">&#x9636;&#x6DF7;&#x5408;&#x77E9;<\/span><\/span><\/span><span style=\"top:-0.7917839999999998em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mord cjk_fallback\">&#x548C;<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.22222em;\">Y<\/span><span class=\"mord cjk_fallback\">&#x7684;<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03148em;\">k<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222222222222222em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.01968em;\">l<\/span><span class=\"mord cjk_fallback\">&#x9636;&#x4E2D;&#x5FC3;&#x77E9;<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:2.8682160000000003em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n\n      <\/div>\n      \n      \n    \n    \n    \n    \n    \n   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