{"id":714,"date":"2023-07-29T00:10:17","date_gmt":"2023-07-29T00:10:17","guid":{"rendered":"https:\/\/statorials.org\/ja\/%e4%ba%8c%e9%a0%85%e5%88%86%e5%b8%83\/"},"modified":"2023-07-29T00:10:17","modified_gmt":"2023-07-29T00:10:17","slug":"%e4%ba%8c%e9%a0%85%e5%88%86%e5%b8%83","status":"publish","type":"post","link":"https:\/\/statorials.org\/ja\/%e4%ba%8c%e9%a0%85%e5%88%86%e5%b8%83\/","title":{"rendered":"\u4e8c\u9805\u5206\u5e03\u306e\u6982\u8981"},"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\u9805\u5206\u5e03\u306f\u3001<\/strong>\u7d71\u8a08\u5b66\u3067\u6700\u3082\u3088\u304f\u4f7f\u308f\u308c\u308b\u5206\u5e03\u306e 1 \u3064\u3067\u3059\u3002\u4e8c\u9805\u5206\u5e03\u3092\u7406\u89e3\u3059\u308b\u306b\u306f\u3001\u307e\u305a<a href=\"https:\/\/statorials.org\/ja\/\u4e8c\u9805\u5b9f\u9a13\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\"binomial experiments (opens in a new tab)\">\u4e8c\u9805\u5b9f\u9a13<\/a>\u3092\u7406\u89e3\u3059\u308b\u3053\u3068\u304c\u5f79\u7acb\u3061\u307e\u3059\u3002<\/p>\n<h3 class=\"wp-block-heading\"><strong>\u4e8c\u9805\u5b9f\u9a13<\/strong><\/h3>\n<p><strong>\u4e8c\u9805\u5b9f\u9a13\u306f<\/strong>\u3001\u6b21\u306e\u7279\u6027\u3092\u6301\u3064\u5b9f\u9a13\u3067\u3059\u3002<\/p>\n<ul>\n<li>\u5b9f\u9a13\u306f<em>n<\/em>\u56de\u7e70\u308a\u8fd4\u3055\u308c\u308b\u8a66\u884c\u3067\u69cb\u6210\u3055\u308c\u307e\u3059\u3002<\/li>\n<li>\u5404\u30c8\u30e9\u30a4\u30a2\u30eb\u3067\u8003\u3048\u3089\u308c\u308b\u7d50\u679c\u306f 2 \u3064\u3060\u3051\u3067\u3059\u3002<\/li>\n<li> <em>p<\/em>\u3067\u793a\u3055\u308c\u308b\u6210\u529f\u306e\u78ba\u7387\u306f\u3001\u5404\u8a66\u884c\u3067\u540c\u3058\u3067\u3059\u3002<\/li>\n<li>\u5404\u30c6\u30b9\u30c8\u306f\u72ec\u7acb\u3057\u3066\u3044\u307e\u3059\u3002<\/li>\n<\/ul>\n<p>\u4e8c\u9805\u5b9f\u9a13\u306e\u6700\u3082\u308f\u304b\u308a\u3084\u3059\u3044\u4f8b\u306f\u3001\u30b3\u30a4\u30f3\u6295\u3052\u3067\u3059\u3002\u305f\u3068\u3048\u3070\u3001\u30b3\u30a4\u30f3\u309210\u56de\u6295\u3052\u305f\u3068\u3057\u307e\u3059\u3002\u6b21\u306e 4 \u3064\u306e\u7279\u6027\u304c\u3042\u308b\u305f\u3081\u3001\u3053\u308c\u306f\u4e8c\u9805\u5b9f\u9a13\u3067\u3059\u3002<\/p>\n<ul>\n<li>\u5b9f\u9a13\u306f<em>n<\/em>\u56de\u7e70\u308a\u8fd4\u3055\u308c\u308b\u8a66\u884c\u3067\u69cb\u6210\u3055\u308c\u307e\u3059\u3002\u8a66\u884c\u306f 10 \u56de\u3042\u308a\u307e\u3059\u3002<\/li>\n<li>\u5404\u30c8\u30e9\u30a4\u30a2\u30eb\u306b\u306f\u3001\u8868\u304b\u88cf\u304b\u306e 2 \u3064\u306e\u7d50\u679c\u3057\u304b\u3042\u308a\u307e\u305b\u3093\u3002<\/li>\n<li> <em>p<\/em>\u3067\u793a\u3055\u308c\u308b\u6210\u529f\u306e\u78ba\u7387\u306f\u3001\u5404\u8a66\u884c\u3067\u540c\u3058\u3067\u3059\u3002 \u300c\u6210\u529f\u300d\u3092\u8868\u306e\u7740\u5730\u3068\u5b9a\u7fa9\u3059\u308b\u3068\u3001\u5404\u8a66\u884c\u306e\u6210\u529f\u78ba\u7387\u306f\u3061\u3087\u3046\u3069 0.5 \u306b\u306a\u308a\u307e\u3059\u3002<\/li>\n<li>\u5404\u30c8\u30e9\u30a4\u30a2\u30eb\u306f\u72ec\u7acb\u3057\u3066\u3044\u307e\u3059\u3002\u3042\u308b\u30b3\u30a4\u30f3\u30c8\u30b9\u306e\u7d50\u679c\u306f\u3001\u4ed6\u306e\u30b3\u30a4\u30f3\u30c8\u30b9\u306e\u7d50\u679c\u306b\u5f71\u97ff\u3092\u4e0e\u3048\u307e\u305b\u3093\u3002<\/li>\n<\/ul>\n<h3 class=\"wp-block-heading\"><strong>\u4e8c\u9805\u5206\u5e03<\/strong><\/h3>\n<p><strong>\u4e8c\u9805\u5206\u5e03\u306f\u3001<\/strong> <em>n<\/em>\u56de\u306e\u4e8c\u9805\u5b9f\u9a13\u3067<em>k<\/em>\u56de\u306e\u6210\u529f\u304c\u5f97\u3089\u308c\u308b\u78ba\u7387\u3092\u8868\u3057\u307e\u3059\u3002<\/p>\n<p> <a href=\"https:\/\/statorials.org\/ja\/\u30e9\u30f3\u30bf\u3099\u30e0\u5909\u6570\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\"random variable (opens in a new tab)\">\u78ba\u7387\u5909\u6570<\/a><em>X \u304c<\/em>\u4e8c\u9805\u5206\u5e03\u306b\u5f93\u3046\u5834\u5408\u3001 <em>X<\/em> = <em>k<\/em>\u304c\u6210\u529f\u3059\u308b\u78ba\u7387\u306f\u6b21\u306e\u5f0f\u3067\u6c42\u3081\u3089\u308c\u307e\u3059\u3002<\/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\uff1a<\/p>\n<ul>\n<li> <strong>n:<\/strong>\u8a66\u884c\u56de\u6570<\/li>\n<li><strong>k:<\/strong>\u6210\u529f\u56de\u6570<\/li>\n<li><strong>p:<\/strong>\u4e0e\u3048\u3089\u308c\u305f\u8a66\u884c\u306e\u6210\u529f\u78ba\u7387<\/li>\n<li><strong><sub>n<\/sub> C <sub>k<\/sub> :<\/strong> <em>n<\/em>\u56de\u306e\u8a66\u884c\u3067<em>k \u500b\u306e<\/em>\u6210\u529f\u3092\u5f97\u308b\u65b9\u6cd5\u306e\u6570<\/li>\n<\/ul>\n<p>\u305f\u3068\u3048\u3070\u3001\u30b3\u30a4\u30f3\u30923\u56de\u6295\u3052\u305f\u3068\u3057\u307e\u3059\u3002\u4e0a\u8a18\u306e\u5f0f\u3092\u4f7f\u7528\u3057\u3066\u3001\u3053\u308c\u3089 3 \u56de\u306e\u30c8\u30b9\u3067 0\u30011\u30012\u3001\u304a\u3088\u3073 3 \u306e\u8868\u304c\u51fa\u308b\u78ba\u7387\u3092\u6c7a\u5b9a\u3067\u304d\u307e\u3059\u3002<\/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<\/em><strong><em>:<\/em><\/strong>\u5404\u4f8b<sub><em>\u306e<\/em><\/sub><sub><em>nCk<\/em><\/sub><em>\u3092\u8a08\u7b97\u3059\u308b\u306b\u306f\u3001\u3053\u306e<a href=\"https:\/\/statorials.org\/ja\/-10\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\"Combination Calculator (opens in a new tab)\">\u7d44\u307f\u5408\u308f\u305b\u8a08\u7b97\u6a5f<\/a>\u3092\u4f7f\u7528\u3057\u307e\u3057\u305f<\/em><em>\u3002<\/em><\/p>\n<p>\u5358\u7d14\u306a\u30d2\u30b9\u30c8\u30b0\u30e9\u30e0\u3092\u4f5c\u6210\u3057\u3066\u3001\u3053\u306e\u78ba\u7387\u5206\u5e03\u3092\u8996\u899a\u5316\u3067\u304d\u307e\u3059\u3002 <\/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\u9805\u5206\u5e03\u30d2\u30b9\u30c8\u30b0\u30e9\u30e0\" class=\"wp-image-7153\" width=\"339\" height=\"335\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h3 class=\"wp-block-heading\"><strong>\u7d2f\u7a4d\u4e8c\u9805\u78ba\u7387\u306e\u8a08\u7b97<\/strong><\/h3>\n<p>\u4e0a\u8a18\u306e\u5f0f\u3092\u4f7f\u7528\u3057\u3066\u5358\u4e00\u306e\u4e8c\u9805\u78ba\u7387 (\u305f\u3068\u3048\u3070\u3001\u30b3\u30a4\u30f3\u304c 3 \u56de\u6295\u3052\u3066 1 \u56de\u8868\u306b\u306a\u308b\u78ba\u7387) \u3092\u8a08\u7b97\u3059\u308b\u306e\u306f\u7c21\u5358\u3067\u3059\u304c\u3001\u7d2f\u7a4d\u7684\u306a\u4e8c\u9805\u78ba\u7387\u3092\u8a08\u7b97\u3059\u308b\u306b\u306f\u3001\u500b\u3005\u306e\u78ba\u7387\u3092\u52a0\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<p>\u305f\u3068\u3048\u3070\u3001\u30b3\u30a4\u30f3\u3092 3 \u56de\u6295\u3052\u3066\u8868\u304c\u51fa\u308b\u78ba\u7387\u3092\u77e5\u308a\u305f\u3044\u3068\u3057\u307e\u3059\u3002\u3053\u306e\u78ba\u7387\u3092\u8a08\u7b97\u3059\u308b\u306b\u306f\u6b21\u306e\u5f0f\u3092\u4f7f\u7528\u3057\u307e\u3059\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>\u8907\u6570\u306e\u78ba\u7387\u3092\u52a0\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u305f\u3081\u3001\u3053\u308c\u306f<strong>\u7d2f\u7a4d<\/strong>\u78ba\u7387\u3068\u547c\u3070\u308c\u307e\u3059\u3002\u540c\u69d8\u306e\u5f0f\u3092\u4f7f\u7528\u3057\u3066\u3001\u7d50\u679c\u3054\u3068\u306b<em>k<\/em>\u4ee5\u4e0b\u306e\u8868\u304c\u5f97\u3089\u308c\u308b\u7d2f\u7a4d\u78ba\u7387\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/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>\u30d2\u30b9\u30c8\u30b0\u30e9\u30e0\u3092\u4f5c\u6210\u3057\u3066\u3001\u3053\u306e\u7d2f\u7a4d\u78ba\u7387\u5206\u5e03\u3092\u8996\u899a\u5316\u3067\u304d\u307e\u3059\u3002 <\/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\u7a4d\u4e8c\u9805\u78ba\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\u9805\u78ba\u7387\u8a08\u7b97\u30c4\u30fc\u30eb<\/strong><\/h3>\n<p>\u5c0f\u3055\u3044\u6570\u3092\u6271\u3046\u5834\u5408 (\u30b3\u30a4\u30f3\u3092 3 \u56de\u6295\u3052\u308b\u306a\u3069)\u3001\u4e8c\u9805\u78ba\u7387\u3092\u624b\u52d5\u3067\u8a08\u7b97\u3059\u308b\u306e\u304c\u5408\u7406\u7684\u3067\u3059\u3002\u305f\u3060\u3057\u3001\u3088\u308a\u5927\u304d\u306a\u6570 (\u4f8b: 100 \u56de\u306e\u5f15\u304d\u5206\u3051) \u3092\u6271\u3046\u5834\u5408\u3001\u78ba\u7387\u3092\u624b\u52d5\u3067\u8a08\u7b97\u3059\u308b\u306e\u306f\u56f0\u96e3\u306a\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306a\u5834\u5408\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u4e8c<strong>\u9805\u78ba\u7387\u8a08\u7b97\u30c4\u30fc\u30eb<\/strong>\u3092\u4f7f\u7528\u3059\u308b\u3068\u4fbf\u5229\u3067\u3059\u3002<\/p>\n<p>\u305f\u3068\u3048\u3070\u3001\u30b3\u30a4\u30f3\u3092 n = 100 \u56de\u6295\u3052\u308b\u3068\u3057\u307e\u3059\u3002\u4e0e\u3048\u3089\u308c\u305f\u8a66\u884c\u3067\u8868\u304c\u51fa\u308b\u78ba\u7387\u306f p = 0.5 \u3067\u3001k = 43 \u56de\u4ee5\u4e0b\u3067\u8868\u304c\u51fa\u308b\u78ba\u7387\u3092\u77e5\u308a\u305f\u3044\u3068\u3057\u307e\u3059\u3002<\/p>\n<div id=\"words\"> <label for=\"p\"><b>p<\/b> (\u7279\u5b9a\u306e\u8a66\u884c\u306e\u6210\u529f\u78ba\u7387)<\/label><input id=\"p\" min=\"0\" type=\"number\" value=\"0.5\"><\/div>\n<div id=\"words\"> <label for=\"n\"><b>n<\/b> (\u8a66\u884c\u56de\u6570)<\/label><input id=\"n\" min=\"0\" type=\"number\" value=\"100\"><\/div>\n<div id=\"words\"> <label for=\"k\"><b>k<\/b> (\u6210\u529f\u56de\u6570)<\/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>\u7d50\u679c\u3092\u89e3\u91c8\u3059\u308b\u65b9\u6cd5\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002<\/p>\n<ul>\n<li>\u30b3\u30a4\u30f3\u304c\u3061\u3087\u3046\u3069 43 \u56de\u8868\u306b\u306a\u308b\u78ba\u7387\u306f<strong>0.03007<\/strong>\u3067\u3059\u3002<\/li>\n<li> 43 \u56de\u672a\u6e80\u3067\u30b3\u30a4\u30f3\u306e\u8868\u304c\u51fa\u308b\u78ba\u7387\u306f<strong>0.06661<\/strong>\u3067\u3059\u3002<\/li>\n<li>\u30b3\u30a4\u30f3\u304c 43 \u56de\u4ee5\u4e0b\u3067\u8868\u306b\u306a\u308b\u78ba\u7387\u306f<strong>0.09667<\/strong>\u3067\u3059\u3002<\/li>\n<li>\u30b3\u30a4\u30f3\u304c 43 \u56de\u4ee5\u4e0a\u8868\u306b\u306a\u308b\u78ba\u7387\u306f<strong>0.90333<\/strong>\u3067\u3059\u3002<\/li>\n<li>\u30b3\u30a4\u30f3\u304c 43 \u56de\u4ee5\u4e0a\u8868\u306b\u306a\u308b\u78ba\u7387\u306f<strong>0.93339<\/strong>\u3067\u3059\u3002<\/li>\n<\/ul>\n<h3 class=\"wp-block-heading\"><strong>\u4e8c\u9805\u5206\u5e03\u306e\u6027\u8cea<\/strong><\/h3>\n<p>\u4e8c\u9805\u5206\u5e03\u306b\u306f\u6b21\u306e\u7279\u6027\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<p>\u5206\u5e03\u306e\u5e73\u5747\u306f<strong>\u03bc = np<\/strong><\/p>\n<p>\u5206\u5e03\u306e\u5206\u6563\u306f<strong>\u03c3<\/strong> <sup><strong>2<\/strong><\/sup> <strong>= np(1-p)<\/strong>\u3067\u3059\u3002<\/p>\n<p>\u5206\u5e03\u306e\u6a19\u6e96\u504f\u5dee\u306f<strong>\u03c3 = \u221a<\/strong> <span style=\"text-decoration: overline;\"><strong>np(1-p)<\/strong><\/span>\u3067\u3059\u3002<\/p>\n<p>\u305f\u3068\u3048\u3070\u3001\u30b3\u30a4\u30f3\u3092 3 \u56de\u6295\u3052\u305f\u3068\u3057\u307e\u3059\u3002 p = \u30b3\u30a4\u30f3\u304c\u8868\u306b\u306a\u308b\u78ba\u7387\u3068\u3057\u307e\u3059\u3002<\/p>\n<p>\u4e88\u60f3\u3055\u308c\u308b\u30d8\u30c3\u30c9\u306e\u5e73\u5747\u6570\u306f \u03bc = np = 3*.5 = <strong>1.5<\/strong>\u3067\u3059\u3002<\/p>\n<p>\u4e88\u60f3\u3055\u308c\u308b\u4eba\u6570\u306e\u5206\u6563\u306f \u03c3 <sup>2<\/sup> = np(1-p) = 3*.5*(1-.5) = <strong>0.75<\/strong>\u3067\u3059\u3002<\/p>\n<h3 class=\"wp-block-heading\"><strong>\u4e8c\u9805\u5206\u5e03\u306e\u7df4\u7fd2\u554f\u984c<\/strong><\/h3>\n<p>\u6b21\u306e\u7df4\u7fd2\u554f\u984c\u3092\u4f7f\u7528\u3057\u3066\u3001\u4e8c\u9805\u5206\u5e03\u306b\u95a2\u3059\u308b\u77e5\u8b58\u3092\u30c6\u30b9\u30c8\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n<p><strong>\u554f\u984c 1<\/strong><\/p>\n<p><strong>\u8cea\u554f:<\/strong>\u30dc\u30d6\u306f\u30d5\u30ea\u30fc\u30b9\u30ed\u30fc\u8a66\u6295\u306e 60% \u3092\u6210\u529f\u3055\u305b\u307e\u3059\u3002\u5f7c\u304c\u30d5\u30ea\u30fc\u30b9\u30ed\u30fc\u3092 12 \u56de\u6210\u529f\u3055\u305b\u305f\u5834\u5408\u3001\u3061\u3087\u3046\u3069 10 \u56de\u6210\u529f\u3059\u308b\u78ba\u7387\u306f\u3069\u308c\u304f\u3089\u3044\u3067\u3059\u304b?<\/p>\n<p><strong>\u56de\u7b54:<\/strong>\u4e0a\u8a18\u306e\u4e8c\u9805\u5206\u5e03\u8a08\u7b97\u30c4\u30fc\u30eb\u3092 p = 0.6\u3001n = 12\u3001k = 10 \u3068\u3057\u3066\u4f7f\u7528\u3059\u308b\u3068\u3001 P(X=10) = <strong>0.06385<\/strong>\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<p><strong>\u554f\u984c 2<\/strong><\/p>\n<p><strong>\u8cea\u554f:<\/strong>\u30b8\u30a7\u30b7\u30ab\u306f\u30b3\u30a4\u30f3\u3092 5 \u56de\u6295\u3052\u307e\u3059\u3002\u30b3\u30a4\u30f3\u306e\u8868\u304c 2 \u56de\u4ee5\u4e0b\u306b\u306a\u308b\u78ba\u7387\u306f\u3044\u304f\u3089\u3067\u3059\u304b?<\/p>\n<p><strong>\u56de\u7b54:<\/strong> p = 0.5\u3001n = 5\u3001k = 2 \u3067\u4e0a\u8a18\u306e\u4e8c\u9805\u5206\u5e03\u8a08\u7b97\u30c4\u30fc\u30eb\u3092\u4f7f\u7528\u3059\u308b\u3068\u3001 P(X\u22642) = <strong>0.5<\/strong>\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<p><strong>\u554f\u984c 3<\/strong><\/p>\n<p><strong>\u8cea\u554f:<\/strong>\u7279\u5b9a\u306e\u5b66\u751f\u304c\u7279\u5b9a\u306e\u5927\u5b66\u306b\u5408\u683c\u3059\u308b\u78ba\u7387\u306f 0.2 \u3067\u3059\u3002 10 \u4eba\u306e\u5b66\u751f\u304c\u5fdc\u52df\u3057\u305f\u5834\u5408\u30014 \u4eba\u4ee5\u4e0a\u304c\u5408\u683c\u3059\u308b\u78ba\u7387\u306f\u3069\u308c\u304f\u3089\u3044\u3067\u3059\u304b?<\/p>\n<p><strong>\u56de\u7b54:<\/strong> p = 0.2\u3001n = 10\u3001k = 4 \u3067\u4e0a\u8a18\u306e\u4e8c\u9805\u5206\u5e03\u8a08\u7b97\u30c4\u30fc\u30eb\u3092\u4f7f\u7528\u3059\u308b\u3068\u3001 P(X&gt;4) = <strong>0.03279<\/strong>\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<p><strong>\u554f\u984c4<\/strong><\/p>\n<p><strong>\u8cea\u554f:<\/strong>\u3042\u306a\u305f\u306f\u30b3\u30a4\u30f3\u3092 12 \u56de\u6295\u3052\u307e\u3059\u3002\u4e88\u60f3\u3055\u308c\u308b\u5e73\u5747\u982d\u6570\u306f\u3069\u308c\u304f\u3089\u3044\u3067\u3059\u304b?<\/p>\n<p><strong>\u56de\u7b54:<\/strong>\u4e8c\u9805\u5206\u5e03\u306e\u5e73\u5747\u306f \u03bc = np \u3068\u3057\u3066\u8a08\u7b97\u3055\u308c\u308b\u3053\u3068\u3092\u601d\u3044\u51fa\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u03bc = 12*0.5 = <strong>6 \u30d8\u30c3\u30c9\u306b\u306a\u308a\u307e\u3059<\/strong>\u3002<\/p>\n<p><strong>\u554f\u984c5<\/strong><\/p>\n<p><strong>\u8cea\u554f:<\/strong>\u30de\u30fc\u30af\u306f\u8a66\u884c\u56de\u6570\u306e 10% \u3067\u30db\u30fc\u30e0\u30e9\u30f3\u3092\u6253\u3063\u3066\u3044\u307e\u3059\u3002\u5f7c\u304c\u7279\u5b9a\u306e\u8a66\u5408\u3067 5 \u56de\u306e\u8a66\u884c\u3092\u6253\u3063\u305f\u5834\u5408\u3001\u5f7c\u304c\u6253\u3063\u305f\u30db\u30fc\u30e0\u30e9\u30f3\u306e\u6570\u306e\u5206\u6563\u306f\u3044\u304f\u3089\u3067\u3059\u304b?<\/p>\n<p><strong>\u56de\u7b54:<\/strong>\u4e8c\u9805\u5206\u5e03\u306e\u5206\u6563\u306f \u03c3 <sup>2<\/sup> = np(1-p) \u3068\u3057\u3066\u8a08\u7b97\u3055\u308c\u308b\u3053\u3068\u3092\u601d\u3044\u51fa\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u3057\u305f\u304c\u3063\u3066\u3001 <sup>\u03c32<\/sup> = 6*.1*(1-.1) = <strong>0.54 \u3068\u306a\u308a\u307e\u3059<\/strong>\u3002<\/p>\n<h3 class=\"wp-block-heading\"><strong>\u8ffd\u52a0\u30ea\u30bd\u30fc\u30b9<\/strong><\/h3>\n<p>\u6b21\u306e\u8a18\u4e8b\u306f\u3001\u3055\u307e\u3056\u307e\u306a\u7d71\u8a08\u30bd\u30d5\u30c8\u30a6\u30a7\u30a2\u3067\u4e8c\u9805\u5206\u5e03\u3092\u4f7f\u7528\u3059\u308b\u65b9\u6cd5\u3092\u5b66\u7fd2\u3059\u308b\u306e\u306b\u5f79\u7acb\u3061\u307e\u3059\u3002<\/p>\n<ul>\n<li> <a href=\"https:\/\/statorials.org\/ja\/\u4e8c\u9805\u5206\u5e03\u30a8\u30af\u30bb\u30eb\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\"How to calculate binomial probabilities in Excel (opens in a new tab)\">Excel \u3067\u4e8c\u9805\u78ba\u7387\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5<\/a><\/li>\n<li><a href=\"https:\/\/statorials.org\/ja\/\u4e8c\u9805\u78ba\u7387-ti-84-\u8a08\u7b97\u6a5f\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\"How to calculate binomial probabilities on a TI-84 calculator (opens in a new tab)\">TI-84 \u96fb\u5353\u3067\u4e8c\u9805\u78ba\u7387\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5<\/a><\/li>\n<li><a href=\"https:\/\/statorials.org\/ja\/-10\/\" target=\"_blank\" rel=\"noreferrer noopener\">R \u3067\u4e8c\u9805\u78ba\u7387\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5<\/a><\/li>\n<li><a href=\"https:\/\/statorials.org\/ja\/\u4e8c\u9805\u5206\u5e03-r-\u3092\u30d5\u309a\u30ed\u30c3\u30c8\u3059\u308b\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\"How to plot a binomial distribution in R (opens in a new tab)\">R \u3067\u4e8c\u9805\u5206\u5e03\u3092\u30d7\u30ed\u30c3\u30c8\u3059\u308b\u65b9\u6cd5<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u4e8c\u9805\u5206\u5e03\u306f\u3001\u7d71\u8a08\u5b66\u3067\u6700\u3082\u3088\u304f\u4f7f\u308f\u308c\u308b\u5206\u5e03\u306e 1 \u3064\u3067\u3059\u3002\u4e8c\u9805\u5206\u5e03\u3092\u7406\u89e3\u3059\u308b\u306b\u306f\u3001\u307e\u305a\u4e8c\u9805\u5b9f\u9a13\u3092\u7406\u89e3\u3059\u308b\u3053\u3068\u304c\u5f79\u7acb\u3061\u307e\u3059\u3002 \u4e8c\u9805\u5b9f\u9a13 \u4e8c\u9805\u5b9f\u9a13\u306f\u3001\u6b21\u306e\u7279\u6027\u3092\u6301\u3064\u5b9f\u9a13\u3067\u3059\u3002 \u5b9f\u9a13\u306fn\u56de\u7e70\u308a\u8fd4\u3055\u308c\u308b\u8a66\u884c\u3067\u69cb\u6210\u3055\u308c\u307e\u3059\u3002 \u5404\u30c8\u30e9 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[16],"tags":[],"class_list":["post-714","post","type-post","status-publish","format-standard","hentry","category-16"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u4e8c\u9805\u5206\u5e03\u306e\u6982\u8981 - \u7d71\u8a08\u5b66<\/title>\n<meta name=\"description\" content=\"\u6b63\u5f0f\u306a\u5b9a\u7fa9\u3068\u3044\u304f\u3064\u304b\u306e\u4f8b\u3092\u542b\u3080\u3001\u4e8c\u9805\u5206\u5e03\u306e\u7c21\u5358\u306a\u7d39\u4ecb\u3002\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/ja\/\u4e8c\u9805\u5206\u5e03\/\" \/>\n<meta property=\"og:locale\" content=\"ja_JP\" 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