{"id":717,"date":"2023-07-29T00:10:17","date_gmt":"2023-07-29T00:10:17","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e4%ba%8c%e9%a1%b9%e5%88%86%e5%b8%83\/"},"modified":"2023-07-29T00:10:17","modified_gmt":"2023-07-29T00:10:17","slug":"%e4%ba%8c%e9%a1%b9%e5%88%86%e5%b8%83","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e4%ba%8c%e9%a1%b9%e5%88%86%e5%b8%83\/","title":{"rendered":"\u4e8c\u9879\u5206\u5e03\u7b80\u4ecb"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><script src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mathjs\/5.1.1\/math.js\"><\/script><script src=\"https:\/\/cdn.jsdelivr.net\/npm\/jstat@latest\/dist\/jstat.min.js\"><\/script><\/p>\n<style>\n@import url('https:\/\/fonts.googleapis.com\/css?family=Droid+Serif|Raleway');<\/p>\n<p>#words {\ncolor: black;\nfont-family: Raleway;\nmax-width: 550px;\nmargin: 25px auto;\nline-height: 1.75;\npadding-left: 100px;\n}<\/p>\n<p>#words label, input {\n    display: inline-block;\n    vertical-align: baseline;\n    width: 350px;\n}<\/p>\n<p>    #button {\n      border: 1px solid;\n      border-radius: 10px;\n      margin-top: 20px;\n      padding: 10px 10px;\n      cursor: pointer;\n      outline: none;\n      background-color: white;\n      color: black;\n      font-family: 'Work Sans', sans-serif;\n      border: 1px solid grey;\n      \/* Green *\/\n    }<\/p>\n<p>    #button:hover {\n      background-color: #f6f6f6;\n      border: 1px solid black;\n    }<\/p>\n<p>p, li {\n  color:#000000;\n  font-size: 19px;\n  font-family: 'Helvetica';\n}<\/p>\n<p>p a {\n  color: #9b59b6 !important;\n}\n<\/style>\n<p class=\"has-text-color\" style=\"color:#000000\"><strong>\u4e8c\u9879\u5f0f\u5206\u5e03<\/strong>\u662f\u7edf\u8ba1\u5b66\u4e2d\u6700\u6d41\u884c\u7684\u5206\u5e03\u4e4b\u4e00\u3002\u8981\u7406\u89e3\u4e8c\u9879\u5f0f\u5206\u5e03\uff0c\u9996\u5148\u4e86\u89e3<a href=\"https:\/\/statorials.org\/cn\/\u4e8c\u9879\u5f0f\u5b9e\u9a8c\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\"binomial experiments (opens in a new tab)\">\u4e8c\u9879\u5f0f\u5b9e\u9a8c<\/a>\u4f1a\u6709\u6240\u5e2e\u52a9\u3002<\/p>\n<h3 class=\"wp-block-heading\"><strong>\u4e8c\u9879\u5f0f\u5b9e\u9a8c<\/strong><\/h3>\n<p><strong>\u4e8c\u9879\u5f0f\u5b9e\u9a8c<\/strong>\u662f\u5177\u6709\u4ee5\u4e0b\u5c5e\u6027\u7684\u5b9e\u9a8c\uff1a<\/p>\n<ul>\n<li>\u8be5\u5b9e\u9a8c\u7531<em>n<\/em>\u6b21\u91cd\u590d\u8bd5\u9a8c\u7ec4\u6210\u3002<\/li>\n<li>\u6bcf\u4e2a\u8bd5\u9a8c\u53ea\u6709\u4e24\u79cd\u53ef\u80fd\u7684\u7ed3\u679c\u3002<\/li>\n<li>\u6bcf\u6b21\u8bd5\u9a8c\u7684\u6210\u529f\u6982\u7387\uff08\u8868\u793a\u4e3a<em>p<\/em> \uff09\u662f\u76f8\u540c\u7684\u3002<\/li>\n<li>\u6bcf\u4e2a\u6d4b\u8bd5\u90fd\u662f\u72ec\u7acb\u7684\u3002<\/li>\n<\/ul>\n<p>\u4e8c\u9879\u5f0f\u5b9e\u9a8c\u6700\u660e\u663e\u7684\u4f8b\u5b50\u662f\u629b\u786c\u5e01\u3002\u4f8b\u5982\uff0c\u5047\u8bbe\u6211\u4eec\u629b\u786c\u5e01 10 \u6b21\u3002\u8fd9\u662f\u4e00\u4e2a\u4e8c\u9879\u5f0f\u5b9e\u9a8c\uff0c\u56e0\u4e3a\u5b83\u5177\u6709\u4ee5\u4e0b\u56db\u4e2a\u5c5e\u6027\uff1a<\/p>\n<ul>\n<li>\u8be5\u5b9e\u9a8c\u7531<em>n<\/em>\u6b21\u91cd\u590d\u8bd5\u9a8c\u7ec4\u6210\u2014\u2014\u5171\u6709 10 \u6b21\u8bd5\u9a8c\u3002<\/li>\n<li>\u6bcf\u6b21\u8bd5\u9a8c\u53ea\u6709\u4e24\u79cd\u53ef\u80fd\u7684\u7ed3\u679c\uff1a\u6b63\u9762\u6216\u53cd\u9762\u3002<\/li>\n<li>\u6bcf\u6b21\u8bd5\u9a8c\u7684\u6210\u529f\u6982\u7387\uff08\u8868\u793a\u4e3a<em>p<\/em> \uff09\u662f\u76f8\u540c\u7684\u3002\u5982\u679c\u6211\u4eec\u5c06\u201c\u6210\u529f\u201d\u5b9a\u4e49\u4e3a\u7740\u9646\u5934\uff0c\u90a3\u4e48\u6bcf\u6b21\u5c1d\u8bd5\u7684\u6210\u529f\u6982\u7387\u6070\u597d\u4e3a 0.5\u3002<\/li>\n<li>\u6bcf\u6b21\u8bd5\u9a8c\u90fd\u662f\u72ec\u7acb\u7684\u2014\u2014\u629b\u4e00\u679a\u786c\u5e01\u7684\u7ed3\u679c\u4e0d\u4f1a\u5f71\u54cd\u4efb\u4f55\u5176\u4ed6\u629b\u786c\u5e01\u7684\u7ed3\u679c\u3002<\/li>\n<\/ul>\n<h3 class=\"wp-block-heading\"><strong>\u4e8c\u9879\u5f0f\u5206\u5e03<\/strong><\/h3>\n<p><strong>\u4e8c\u9879\u5f0f\u5206\u5e03<\/strong>\u63cf\u8ff0\u4e86\u5728<em>n\u6b21<\/em>\u4e8c\u9879\u5f0f\u5b9e\u9a8c\u4e2d\u83b7\u5f97<em>k\u6b21<\/em>\u6210\u529f\u7684\u6982\u7387\u3002<\/p>\n<p>\u5982\u679c<a href=\"https:\/\/statorials.org\/cn\/\u968f\u673a\u53d8\u91cf-1\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\"random variable (opens in a new tab)\">\u968f\u673a\u53d8\u91cf<\/a><em>X<\/em>\u670d\u4ece\u4e8c\u9879\u5f0f\u5206\u5e03\uff0c\u5219<em>X<\/em> = <em>k<\/em>\u6210\u529f\u7684\u6982\u7387\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u516c\u5f0f\u6c42\u51fa\uff1a<\/p>\n<p> <strong>P(X=k) = <sub>n<\/sub> C <sub>k<\/sub> * p <sup>k<\/sup> * (1-p) <sup>nk<\/sup><\/strong><\/p>\n<p>\u91d1\u5b50\uff1a<\/p>\n<ul>\n<li> <strong>n\uff1a<\/strong>\u8bd5\u9a8c\u6b21\u6570<\/li>\n<li><strong>k\uff1a<\/strong>\u6210\u529f\u6b21\u6570<\/li>\n<li><strong>p\uff1a<\/strong>\u7ed9\u5b9a\u8bd5\u9a8c\u7684\u6210\u529f\u6982\u7387<\/li>\n<li><strong><sub>n<\/sub> C <sub>k<\/sub> \uff1a<\/strong>\u5728<em>n<\/em>\u6b21\u8bd5\u9a8c\u4e2d\u83b7\u5f97<em>k\u6b21<\/em>\u6210\u529f\u7684\u65b9\u6cd5\u6570<\/li>\n<\/ul>\n<p>\u4f8b\u5982\uff0c\u5047\u8bbe\u6211\u4eec\u629b\u786c\u5e01 3 \u6b21\u3002\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u4e0a\u9762\u7684\u516c\u5f0f\u6765\u786e\u5b9a\u8fd9 3 \u6b21\u629b\u63b7\u4e2d\u83b7\u5f97 0\u30011\u30012 \u548c 3 \u6b21\u6b63\u9762\u671d\u4e0a\u7684\u6982\u7387\uff1a<\/p>\n<p> <strong>P(X=0)<\/strong> = <sub>3<\/sub> C <sub>0<\/sub> * 0.5 <sup>0<\/sup> * (1-0.5) <sup>3-0<\/sup> = 1 * 1 * (0.5) <sup>3<\/sup> = <strong>0.125<\/strong><\/p>\n<p> <strong>P(X=1)<\/strong> = <sub>3<\/sub> C <sub>1<\/sub> * 0.5 <sup>1<\/sup> * (1-0.5) <sup>3-1<\/sup> = 3 * 0.5 * (0.5) <sup>2<\/sup> = <strong>0.375<\/strong><\/p>\n<p> <strong>P(X=2)<\/strong> = <sub>3<\/sub> C <sub>2<\/sub> * 0.5 <sup>2<\/sup> * (1-0.5) <sup>3-2<\/sup> = 3 * 0.25 * (0.5) <sup>1<\/sup> = <strong>0.375<\/strong><\/p>\n<p> <strong>P(X=3)<\/strong> = <sub>3<\/sub> C <sub>3<\/sub> * 0.5 <sup>3<\/sup> * (1-0.5) <sup>3-3<\/sup> = 1 * 0.125 * (0.5) <sup>0<\/sup> = <strong>0.125<\/strong><\/p>\n<p><em>\u6ce8\u610f<\/em><strong><em>\uff1a<\/em><\/strong><em>\u6211\u4eec\u4f7f\u7528\u8fd9\u4e2a<a href=\"https:\/\/statorials.org\/cn\/\u7edf\u8ba1\u5b66\u4ee5\u7b80\u5355\u76f4\u63a5\u7684\u65b9\u5f0f\u89e3\u91ca\u6982\u5ff5\uff0c\u6211\u4eec\u4f7f\u5b66\u4e60\u7edf\u8ba1\u53d8\u5f97\u66f4\u5bb9\u6613\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\"Combination Calculator (opens in a new tab)\">\u7ec4\u5408\u8ba1\u7b97\u5668<\/a>\u6765\u8ba1\u7b97<\/em>\u6bcf\u4e2a\u793a\u4f8b<sub><em>\u7684<\/em><\/sub><sub><em>nCk<\/em><\/sub> <em>\u3002<\/em><\/p>\n<p>\u6211\u4eec\u53ef\u4ee5\u521b\u5efa\u4e00\u4e2a\u7b80\u5355\u7684\u76f4\u65b9\u56fe\u6765\u53ef\u89c6\u5316\u6b64\u6982\u7387\u5206\u5e03\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/binomdist1.png\" alt=\"\u4e8c\u9879\u5f0f\u5206\u5e03\u76f4\u65b9\u56fe\" class=\"wp-image-7153\" width=\"339\" height=\"335\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h3 class=\"wp-block-heading\"><strong>\u7d2f\u79ef\u4e8c\u9879\u5f0f\u6982\u7387\u7684\u8ba1\u7b97<\/strong><\/h3>\n<p>\u4f7f\u7528\u4e0a\u9762\u7684\u516c\u5f0f\u8ba1\u7b97\u5355\u4e2a\u4e8c\u9879\u5f0f\u6982\u7387\uff08\u4f8b\u5982\uff0c\u786c\u5e01 3 \u6b21\u629b\u63b7 1 \u6b21\u6b63\u9762\u671d\u4e0a\u7684\u6982\u7387\uff09\u5f88\u7b80\u5355\uff0c\u4f46\u8981\u8ba1\u7b97\u7d2f\u79ef\u4e8c\u9879\u5f0f\u6982\u7387\uff0c\u6211\u4eec\u9700\u8981\u6dfb\u52a0\u5404\u4e2a\u6982\u7387\u3002<\/p>\n<p>\u4f8b\u5982\uff0c\u5047\u8bbe\u6211\u4eec\u60f3\u77e5\u9053\u4e00\u679a\u786c\u5e01\u5728 3 \u6b21\u629b\u63b7\u4e2d\u51fa\u73b0 1 \u6b21\u6216\u66f4\u5c11\u7684\u6b63\u9762\u671d\u4e0a\u7684\u6982\u7387\u3002\u6211\u4eec\u5c06\u4f7f\u7528\u4ee5\u4e0b\u516c\u5f0f\u6765\u8ba1\u7b97\u8be5\u6982\u7387\uff1a<\/p>\n<p> <strong>P(X\u22641)<\/strong> = P(X=0) + P(X=1) = 0.125 + 0.375 = <strong>0.5<\/strong> \u3002<\/p>\n<p>\u8fd9\u79f0\u4e3a<strong>\u7d2f\u79ef\u6982\u7387<\/strong>\uff0c\u56e0\u4e3a\u5b83\u6d89\u53ca\u6dfb\u52a0\u591a\u4e2a\u6982\u7387\u3002\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u7c7b\u4f3c\u7684\u516c\u5f0f\u8ba1\u7b97\u6bcf\u4e2a\u7ed3\u679c\u83b7\u5f97<em>k \u4e2a<\/em>\u6216\u66f4\u5c11\u6b63\u9762\u671d\u4e0a\u7684\u7d2f\u79ef\u6982\u7387\uff1a<\/p>\n<p> <strong>P(X\u22640)<\/strong> = P(X=0) = <strong>0.125<\/strong> \u3002<\/p>\n<p> <strong>P(X\u22641)<\/strong> = P(X=0) + P(X=1) = 0.125 + 0.375 = <strong>0.5<\/strong> \u3002<\/p>\n<p> <strong>P(X\u22642)<\/strong> = P(X=0) + P(X=1) + P(X=2) = 0.125 + 0.375 + 0.375 = <strong>0.875<\/strong> \u3002<\/p>\n<p> <strong>P(X\u22643)<\/strong> = P(X=0) + P(X=1) + P(X=2) + P(X=3) = 0.125 + 0.375 + 0.375 + 0.125 = <strong>1<\/strong> \u3002<\/p>\n<p>\u6211\u4eec\u53ef\u4ee5\u521b\u5efa\u4e00\u4e2a\u76f4\u65b9\u56fe\u6765\u53ef\u89c6\u5316\u8fd9\u4e2a\u7d2f\u79ef\u6982\u7387\u5206\u5e03\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/binomdist2.png\" alt=\"\u7d2f\u79ef\u4e8c\u9879\u5f0f\u6982\u7387\u5206\u5e03\" class=\"wp-image-7161\" width=\"346\" height=\"341\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h3 class=\"wp-block-heading\"><strong>\u4e8c\u9879\u5f0f\u6982\u7387\u8ba1\u7b97\u5668<\/strong><\/h3>\n<p>\u5f53\u6211\u4eec\u5904\u7406\u5c0f\u6570\u5b57\u65f6\uff08\u4f8b\u5982 3 \u6b21\u786c\u5e01\u629b\u63b7\uff09\uff0c\u624b\u52a8\u8ba1\u7b97\u4e8c\u9879\u5f0f\u6982\u7387\u662f\u5408\u7406\u7684\u3002\u7136\u800c\uff0c\u5f53\u6211\u4eec\u5904\u7406\u8f83\u5927\u7684\u6570\u5b57\uff08\u4f8b\u5982 100 \u6b21\u62bd\u5956\uff09\u65f6\uff0c\u624b\u52a8\u8ba1\u7b97\u6982\u7387\u53ef\u80fd\u4f1a\u5f88\u56f0\u96be\u3002\u5728\u8fd9\u4e9b\u60c5\u51b5\u4e0b\uff0c\u4f7f\u7528\u5982\u4e0b\u6240\u793a\u7684<strong>\u4e8c\u9879\u5f0f\u6982\u7387\u8ba1\u7b97\u5668<\/strong>\u4f1a\u5f88\u6709\u5e2e\u52a9\u3002<\/p>\n<p>\u4f8b\u5982\uff0c\u5047\u8bbe\u6211\u4eec\u629b\u4e00\u679a\u786c\u5e01 n = 100 \u6b21\uff0c\u5728\u7ed9\u5b9a\u7684\u8bd5\u9a8c\u4e2d\uff0c\u5b83\u843d\u5728\u6b63\u9762\u7684\u6982\u7387\u4e3a p = 0.5\uff0c\u6211\u4eec\u60f3\u77e5\u9053\u5b83\u843d\u5728\u6b63\u9762\u7684\u6982\u7387 k = 43 \u6b21\u6216\u66f4\u5c11\uff1a<\/p>\n<div id=\"words\"> <label for=\"p\"><b>p<\/b> \uff08\u7ed9\u5b9a\u8bd5\u9a8c\u7684\u6210\u529f\u6982\u7387\uff09<\/label><input id=\"p\" min=\"0\" type=\"number\" value=\"0.5\"><\/div>\n<div id=\"words\"> <label for=\"n\"><b>n<\/b> \uff08\u8bd5\u9a8c\u6b21\u6570\uff09<\/label><input id=\"n\" min=\"0\" type=\"number\" value=\"100\"><\/div>\n<div id=\"words\"> <label for=\"k\"><b>k<\/b> \uff08\u6210\u529f\u6b21\u6570\uff09<\/label> <input id=\"k\" min=\"0\" type=\"number\" value=\"43\"><\/div>\n<div id=\"words\"><input id=\"button\" type=\"button\" value=\"Calculate\" onclick=\"pvalue()\"><\/div>\n<div id=\"words\">\n<p> P(X= <span id=\"k1\">43<\/span> ) = <span id=\"exactProb\">0.03007<\/span><\/p>\n<p> P(X&lt; <span id=\"k2\">43<\/span> ) = <span id=\"lessProb\">0.06661<\/span><\/p>\n<p> P( <span id=\"k3\">X\u226443<\/span> )= <span id=\"lessEProb\">0.09667<\/span><\/p>\n<p> P(X&gt; <span id=\"k4\">43<\/span> ) = <span id=\"greaterProb\">0.90333<\/span><\/p>\n<p> P( <span id=\"k5\">X\u226543<\/span> ) = <span id=\"greaterEProb\">0.93339<\/span><\/p>\n<\/div>\n<p><script><\/p>\n<p>function pvalue() {<\/p>\n<p>\/\/get input values\nvar p = document.getElementById('p').value*1;\nvar n = document.getElementById('n').value*1;\nvar k = document.getElementById('k').value*1;<\/p>\n<p>\/\/assign probabilities to variable names\nvar exactProb = jStat.binomial.pdf(k,n,p);\nvar lessProb = jStat.binomial.cdf(k-1,n,p);\nvar lessEProb = jStat.binomial.cdf(k,n,p);\nvar greaterProb = 1-jStat.binomial.cdf(k,n,p);\nvar greaterEProb = 1-jStat.binomial.cdf(k-1,n,p);<\/p>\n<p>\/\/output probabilities\ndocument.getElementById('k1').innerHTML = k;\ndocument.getElementById('k2').innerHTML = k;\ndocument.getElementById('k3').innerHTML = k;\ndocument.getElementById('k4').innerHTML = k;\ndocument.getElementById('k5').innerHTML = k;<\/p>\n<p>document.getElementById('exactProb').innerHTML = exactProb.toFixed(5);\ndocument.getElementById('lessProb').innerHTML = lessProb.toFixed(5);\ndocument.getElementById('lessEProb').innerHTML = lessEProb.toFixed(5);\ndocument.getElementById('greaterProb').innerHTML = greaterProb.toFixed(5);\ndocument.getElementById('greaterEProb').innerHTML = greaterEProb.toFixed(5);\n}\n<\/script><\/p>\n<p>\u4ee5\u4e0b\u662f\u5982\u4f55\u89e3\u91ca\u7ed3\u679c\uff1a<\/p>\n<ul>\n<li>\u786c\u5e01\u51fa\u73b0 43 \u6b21\u6b63\u9762\u7684\u6982\u7387\u662f<strong>0.03007<\/strong> \u3002<\/li>\n<li>\u786c\u5e01\u6b63\u9762\u671d\u4e0a\u5c11\u4e8e 43 \u6b21\u7684\u6982\u7387\u662f<strong>0.06661<\/strong> \u3002<\/li>\n<li>\u786c\u5e01\u6b63\u9762\u671d\u4e0a 43 \u6b21\u6216\u66f4\u5c11\u7684\u6982\u7387\u4e3a<strong>0.09667<\/strong> \u3002<\/li>\n<li>\u786c\u5e01\u6b63\u9762\u671d\u4e0a\u8d85\u8fc7 43 \u6b21\u7684\u6982\u7387\u662f<strong>0.90333<\/strong> \u3002<\/li>\n<li>\u786c\u5e01\u6b63\u9762\u671d\u4e0a 43 \u6b21\u6216\u4ee5\u4e0a\u7684\u6982\u7387\u4e3a<strong>0.93339<\/strong> \u3002<\/li>\n<\/ul>\n<h3 class=\"wp-block-heading\"><strong>\u4e8c\u9879\u5206\u5e03\u7684\u6027\u8d28<\/strong><\/h3>\n<p>\u4e8c\u9879\u5f0f\u5206\u5e03\u5177\u6709\u4ee5\u4e0b\u6027\u8d28\uff1a<\/p>\n<p>\u5206\u5e03\u7684\u5e73\u5747\u503c\u4e3a<strong>\u03bc = np<\/strong><\/p>\n<p>\u5206\u5e03\u7684\u65b9\u5dee\u4e3a<strong>\u03c3<\/strong> <sup><strong>2<\/strong><\/sup> <strong>= np(1-p)<\/strong><\/p>\n<p>\u5206\u5e03\u7684\u6807\u51c6\u5dee\u4e3a<strong>\u03c3 = \u221a<\/strong> <span style=\"text-decoration: overline;\"><strong>np(1-p)<\/strong><\/span><\/p>\n<p>\u4f8b\u5982\uff0c\u5047\u8bbe\u6211\u4eec\u629b\u4e00\u679a\u786c\u5e01 3 \u6b21\u3002\u8bbe p = \u786c\u5e01\u6b63\u9762\u671d\u4e0a\u7684\u6982\u7387\u3002<\/p>\n<p>\u6211\u4eec\u671f\u671b\u7684\u5e73\u5747\u5934\u6570\u662f \u03bc = np = 3*.5 = <strong>1.5<\/strong> \u3002<\/p>\n<p>\u6211\u4eec\u671f\u671b\u7684\u4eba\u6570\u65b9\u5dee\u4e3a \u03c3 <sup>2<\/sup> = np(1-p) = 3*.5*(1-.5) = <strong>0.75<\/strong> \u3002<\/p>\n<h3 class=\"wp-block-heading\"><strong>\u4e8c\u9879\u5f0f\u5206\u5e03\u7ec3\u4e60\u9898<\/strong><\/h3>\n<p>\u4f7f\u7528\u4ee5\u4e0b\u7ec3\u4e60\u9898\u6765\u6d4b\u8bd5\u60a8\u5bf9\u4e8c\u9879\u5f0f\u5206\u5e03\u7684\u4e86\u89e3\u3002<\/p>\n<p><strong>\u95ee\u98981<\/strong><\/p>\n<p><strong>\u95ee\u9898\uff1a<\/strong>\u9c8d\u52c3\u7684\u7f5a\u7403\u547d\u4e2d\u7387\u4e3a 60%\u3002\u5982\u679c\u4ed6\u7f5a\u7403 12 \u6b21\uff0c\u4ed6\u7f5a\u4e2d 10 \u6b21\u7684\u6982\u7387\u662f\u591a\u5c11\uff1f<\/p>\n<p><strong>\u7b54\u6848\uff1a<\/strong>\u4f7f\u7528\u4e0a\u9762\u7684\u4e8c\u9879\u5f0f\u5206\u5e03\u8ba1\u7b97\u5668\uff0c\u5176\u4e2d p = 0.6\u3001n = 12 \u548c k = 10\uff0c\u6211\u4eec\u53d1\u73b0 P(X=10) = <strong>0.06385<\/strong> \u3002<\/p>\n<p><strong>\u95ee\u98982<\/strong><\/p>\n<p><strong>\u95ee\u9898\uff1a<\/strong>\u6770\u897f\u5361\u629b\u786c\u5e01 5 \u6b21\u3002\u786c\u5e01\u6b63\u9762\u671d\u4e0a\u4e24\u6b21\u6216\u66f4\u5c11\u7684\u6982\u7387\u662f\u591a\u5c11\uff1f<\/p>\n<p><strong>\u7b54\u6848\uff1a<\/strong>\u4f7f\u7528\u4e0a\u9762\u7684\u4e8c\u9879\u5f0f\u5206\u5e03\u8ba1\u7b97\u5668\uff0cp = 0.5\u3001n = 5 \u548c k = 2\uff0c\u6211\u4eec\u53d1\u73b0 P(X\u22642) = <strong>0.5<\/strong> \u3002<\/p>\n<p><strong>\u95ee\u98983<\/strong><\/p>\n<p><strong>\u95ee\u9898\uff1a<\/strong>\u67d0\u4e2a\u5b66\u751f\u88ab\u67d0\u6240\u5927\u5b66\u5f55\u53d6\u7684\u6982\u7387\u662f 0.2\u3002\u5982\u679c\u6709 10 \u540d\u5b66\u751f\u7533\u8bf7\uff0c\u8d85\u8fc7 4 \u540d\u5b66\u751f\u88ab\u5f55\u53d6\u7684\u6982\u7387\u662f\u591a\u5c11\uff1f<\/p>\n<p><strong>\u7b54\u6848\uff1a<\/strong>\u4f7f\u7528\u4e0a\u9762\u7684\u4e8c\u9879\u5f0f\u5206\u5e03\u8ba1\u7b97\u5668\uff0c\u5176\u4e2d p = 0.2\u3001n = 10 \u4e14 k = 4\uff0c\u6211\u4eec\u53d1\u73b0 P(X&gt;4) = <strong>0.03279<\/strong> \u3002<\/p>\n<p><strong>\u95ee\u98984<\/strong><\/p>\n<p><strong>\u95ee\u9898\uff1a<\/strong>\u629b\u786c\u5e01 12 \u6b21\u3002\u9884\u8ba1\u51fa\u73b0\u7684\u5e73\u5747\u5934\u50cf\u6570\u662f\u591a\u5c11\uff1f<\/p>\n<p><strong>\u7b54\u6848\uff1a<\/strong>\u56de\u60f3\u4e00\u4e0b\uff0c\u4e8c\u9879\u5f0f\u5206\u5e03\u7684\u5747\u503c\u8ba1\u7b97\u516c\u5f0f\u4e3a \u03bc = np\u3002\u56e0\u6b64\uff0c\u03bc = 12*0.5 = <strong>6 \u4e2a\u5934<\/strong>\u3002<\/p>\n<p><strong>\u95ee\u98985<\/strong><\/p>\n<p><strong>\u95ee\u9898\uff1a<\/strong>\u9a6c\u514b\u6709 10% \u7684\u51fa\u624b\u6b21\u6570\u80fd\u6253\u51fa\u5168\u5792\u6253\u3002\u5982\u679c\u4ed6\u5728\u4e00\u573a\u6bd4\u8d5b\u4e2d\u51fa\u51fb 5 \u6b21\uff0c\u4ed6\u51fb\u4e2d\u7684\u672c\u5792\u6253\u6570\u91cf\u7684\u5dee\u5f02\u662f\u591a\u5c11\uff1f<\/p>\n<p><strong>\u7b54\u6848\uff1a<\/strong>\u56de\u60f3\u4e00\u4e0b\uff0c\u4e8c\u9879\u5f0f\u5206\u5e03\u7684\u65b9\u5dee\u8ba1\u7b97\u516c\u5f0f\u4e3a \u03c3 <sup>2<\/sup> = np(1-p)\u3002\u56e0\u6b64\uff0c <sup>\u03c32<\/sup> = 6*.1*(1-.1) = <strong>0.54<\/strong> \u3002<\/p>\n<h3 class=\"wp-block-heading\"><strong>\u5176\u4ed6\u8d44\u6e90<\/strong><\/h3>\n<p>\u4ee5\u4e0b\u6587\u7ae0\u53ef\u4ee5\u5e2e\u52a9\u60a8\u5b66\u4e60\u5982\u4f55\u5728\u4e0d\u540c\u7684\u7edf\u8ba1\u8f6f\u4ef6\u4e2d\u4f7f\u7528\u4e8c\u9879\u5206\u5e03\uff1a<\/p>\n<ul>\n<li> <a href=\"https:\/\/statorials.org\/cn\/\u4e8c\u9879\u5f0f\u5206\u5e03excel\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\"How to calculate binomial probabilities in Excel (opens in a new tab)\">\u5982\u4f55\u5728 Excel \u4e2d\u8ba1\u7b97\u4e8c\u9879\u5f0f\u6982\u7387<\/a><\/li>\n<li><a href=\"https:\/\/statorials.org\/cn\/\u4e8c\u9879\u5f0f\u6982\u7387-ti-84-\u8ba1\u7b97\u5668\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\"How to calculate binomial probabilities on a TI-84 calculator (opens in a new tab)\">\u5982\u4f55\u5728 TI-84 \u8ba1\u7b97\u5668\u4e0a\u8ba1\u7b97\u4e8c\u9879\u5f0f\u6982\u7387<\/a><\/li>\n<li><a href=\"https:\/\/statorials.org\/cn\/\u7edf\u8ba1\u5b66\u4ee5\u7b80\u5355\u76f4\u63a5\u7684\u65b9\u5f0f\u89e3\u91ca\u6982\u5ff5\uff0c\u6211\u4eec\u4f7f\u5b66\u4e60\u7edf\u8ba1\u53d8\u5f97\u66f4\u5bb9\u6613\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u5982\u4f55\u5728 R \u4e2d\u8ba1\u7b97\u4e8c\u9879\u5f0f\u6982\u7387<\/a><\/li>\n<li><a href=\"https:\/\/statorials.org\/cn\/\u7ed8\u5236\u4e8c\u9879\u5f0f\u5206\u5e03-r\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\"How to plot a binomial distribution in R (opens in a new tab)\">\u5982\u4f55\u5728 R \u4e2d\u7ed8\u5236\u4e8c\u9879\u5f0f\u5206\u5e03<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u4e8c\u9879\u5f0f\u5206\u5e03\u662f\u7edf\u8ba1\u5b66\u4e2d\u6700\u6d41\u884c\u7684\u5206\u5e03\u4e4b\u4e00\u3002\u8981\u7406\u89e3\u4e8c\u9879\u5f0f\u5206\u5e03\uff0c\u9996\u5148\u4e86\u89e3\u4e8c\u9879\u5f0f\u5b9e\u9a8c\u4f1a\u6709\u6240\u5e2e\u52a9\u3002 \u4e8c\u9879\u5f0f\u5b9e\u9a8c \u4e8c\u9879\u5f0f\u5b9e\u9a8c [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-717","post","type-post","status-publish","format-standard","hentry","category-11"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u4e8c\u9879\u5f0f\u5206\u5e03\u7b80\u4ecb - Statorials<\/title>\n<meta name=\"description\" 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