{"id":6165,"date":"2022-05-10T15:49:58","date_gmt":"2022-05-10T06:49:58","guid":{"rendered":"https:\/\/hatsudy.com\/jp\/?p=6165"},"modified":"2022-05-28T21:18:26","modified_gmt":"2022-05-28T12:18:26","slug":"bernoulli","status":"publish","type":"post","link":"https:\/\/hatsudy.com\/jp\/bernoulli.html","title":{"rendered":"\u30d9\u30eb\u30cc\u30fc\u30a4\u5206\u5e03\uff1a\u671f\u5f85\u5024\u30fb\u5206\u6563\u306e\u8a08\u7b97\u3068\u4e8c\u9805\u5206\u5e03\u3068\u306e\u9055\u3044"},"content":{"rendered":"\n<p>\u4e8c\u8005\u629e\u4e00\uff08\u7d50\u679c\u304c2\u3064\u306e\u307f\uff09\u306e\u30b1\u30fc\u30b9\u306f\u591a\u3044\u3067\u3059\u3002\u7d50\u679c\u304c2\u3064\u306e\u3068\u304d\u3001\u7d71\u8a08\u5b66\u3067\u306f\u30d9\u30eb\u30cc\u30fc\u30a4\u5206\u5e03\u3092\u5229\u7528\u3057\u307e\u3059\u3002\u30d9\u30eb\u30cc\u30fc\u30a4\u5206\u5e03\u306e\u6982\u5ff5\u306f\u7c21\u5358\u3067\u3042\u308a\u3001\u7d50\u679c\u304c2\u3064\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\u3059\u308c\u3070\u3044\u3044\u3067\u3059\u3002<\/p>\n<p>\u7d50\u679c\u304c2\u3064\u3060\u3051\u3067\u3042\u308b\u305f\u3081\u3001\u30d9\u30eb\u30cc\u30fc\u30a4\u5206\u5e03\u306e\u671f\u5f85\u5024\u3092\u5f97\u308b\u65b9\u6cd5\u306f\u7c21\u5358\u3067\u3059\u3002\u4e00\u56de\u306e\u8a66\u884c\u3092\u3059\u308b\u3068\u304d\u306e\u78ba\u7387\u304c\u671f\u5f85\u5024\u306b\u306a\u308a\u307e\u3059\u3002\u30d9\u30eb\u30cc\u30fc\u30a4\u5206\u5e03\u3068\u3044\u3046\u306e\u306f\u3001\u4f55\u5ea6\u3082\u8a66\u884c\u3092\u7e70\u308a\u8fd4\u3059\u306e\u3067\u306f\u306a\u304f\u3001\u4e00\u56de\u306e\u8a66\u884c\u3067\u306e\u5206\u5e03\u3092\u6307\u3057\u307e\u3059\u3002<\/p>\n<p>\u306a\u304a\u3001\u4e8c\u8005\u629e\u4e00\u306e\u78ba\u7387\u3092\u5229\u7528\u3059\u308b\u5206\u5e03\u3068\u3057\u3066\u306f\u4e8c\u9805\u5206\u5e03\u304c\u3042\u308a\u307e\u3059\u3002\u30d9\u30eb\u30cc\u30fc\u30a4\u5206\u5e03\u3068\u4e8c\u9805\u5206\u5e03\u306f\u4f55\u304c\u9055\u3046\u306e\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<p>\u6982\u5ff5\u306f\u7c21\u5358\u3067\u3042\u308b\u3082\u306e\u306e\u3001\u591a\u304f\u306e\u4eba\u306b\u3068\u3063\u3066\u30d9\u30eb\u30cc\u30fc\u30a4\u5206\u5e03\u3068\u3044\u3046\u8a00\u8449\u306f\u306a\u3058\u307f\u304c\u3042\u308a\u307e\u305b\u3093\u3002\u305d\u3053\u3067\u3001\u30d9\u30eb\u30cc\u30fc\u30a4\u5206\u5e03\u3068\u306f\u4f55\u304b\u3092\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<h2>\u7d50\u679c\u304c2\u3064\u3060\u3051\u306e\u8a66\u884c\u304c\u30d9\u30eb\u30cc\u30fc\u30a4\u8a66\u884c<\/h2>\n<p>\u4e8c\u8005\u629e\u4e00\uff08\u7d50\u679c\u304c2\u3064\u3060\u3051\uff09\u306e\u5834\u9762\u306f\u591a\u3044\u3067\u3059\u3002\u4f8b\u3048\u3070\u3001\u4ee5\u4e0b\u306e\u30b1\u30fc\u30b9\u3067\u306f\u7d50\u679c\u304c2\u3064\u3067\u3059\u3002<\/p>\n<ul>\n<li>\u30b3\u30a4\u30f3\u3092\u6295\u3052\u308b\u3068\u304d\uff1a\u7d50\u679c\u306f\u8868\u3001\u307e\u305f\u306f\u88cf<\/li>\n<li>\u30b5\u30a4\u30b3\u30ed\u3092\u6295\u3052\u308b\u3068\u304d\uff1a1\u306e\u76ee\u3001\u307e\u305f\u306f\u305d\u308c\u4ee5\u5916<\/li>\n<li>\u88fd\u54c1\u306e\u54c1\u8cea\u30c1\u30a7\u30c3\u30af\uff1a\u5408\u683c\u54c1\u3001\u307e\u305f\u306f\u4e0d\u826f\u54c1<\/li>\n<\/ul>\n<p><span style=\"color: #0000ff;\">\u7d50\u679c\u304c2\u3064\u3060\u3051\u306e\u8a66\u884c\u3092\u4e00\u56de\u884c\u3046\u3068\u304d\u3001\u5f97\u3089\u308c\u308b\u5206\u5e03\u304c\u30d9\u30eb\u30cc\u30fc\u30a4\u5206\u5e03\u3067\u3059\u3002<\/span>\u30d9\u30eb\u30cc\u30fc\u30a4\u5206\u5e03\u3067\u306f\u7d50\u679c\u304c2\u3064\u3060\u3051\u306a\u306e\u3067\u3001\u78ba\u7387\u5909\u6570\u306f0\u307e\u305f\u306f1\u3067\u3059\u3002<\/p>\n<p>\u4f8b\u3048\u3070\u30b5\u30a4\u30b3\u30ed\u3092\u6295\u3052\u30011\u306e\u76ee\u304c\u51fa\u305f\u3089\u78ba\u7387\u5909\u65700\uff08\u5931\u6557\uff09\u30011\u4ee5\u5916\u306e\u76ee\u304c\u51fa\u305f\u3089\u78ba\u7387\u5909\u65701\uff08\u6210\u529f\uff09\u3068\u3057\u307e\u3059\u30021\u306e\u76ee\u304c\u51fa\u308b\u78ba\u7387\u306f\\(\\displaystyle\\frac{1}{6}\\)\u3067\u3059\u3002\u307e\u305f\u30011\u4ee5\u5916\u306e\u76ee\u304c\u51fa\u308b\u78ba\u7387\u306f\\(\\displaystyle\\frac{5}{6}\\)\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u30d9\u30eb\u30cc\u30fc\u30a4\u5206\u5e03\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/05\/jfwj14.jpg\" alt=\"\" width=\"400\" height=\"298\" class=\"aligncenter size-full wp-image-6202\" \/><\/p>\n<p>\u901a\u5e38\u3001\u7d71\u8a08\u30c7\u30fc\u30bf\u3092\u96c6\u3081\u308b\u3068\u304d\u306f\u8907\u6570\u306e\u30b5\u30f3\u30d7\u30eb\u3092\u5229\u7528\u3057\u307e\u3059\u3002\u305f\u3060\u30d9\u30eb\u30cc\u30fc\u30a4\u5206\u5e03\u3067\u306f\u3001\u4e00\u3064\u306e\u8a66\u884c\u306e\u7d50\u679c\u3092\u5229\u7528\u3057\u307e\u3059\u3002<\/p>\n<h3>\u30d9\u30eb\u30cc\u30fc\u30a4\u8a66\u884c\u306b\u3088\u3063\u3066\u5f97\u3089\u308c\u308b\u5206\u5e03\uff1a\u30d9\u30eb\u30cc\u30fc\u30a4\u5206\u5e03\u306e\u516c\u5f0f<\/h3>\n<p>\u4e8c\u8005\u629e\u4e00\u306e\u7d50\u679c\u3092\u5f97\u3089\u308c\u308b\u3068\u304d\u3001\u3053\u308c\u3092<span style=\"color: #ff0000;\">\u30d9\u30eb\u30cc\u30fc\u30a4\u8a66\u884c<\/span>\u3068\u3044\u3044\u307e\u3059\u3002\u30d9\u30eb\u30cc\u30fc\u30a4\u5206\u5e03\u3068\u3044\u3046\u306e\u306f\u3001\u30d9\u30eb\u30cc\u30fc\u30a4\u8a66\u884c\u3092\u4e00\u56de\u884c\u3046\u3053\u3068\u306b\u3088\u3063\u3066\u5f97\u3089\u308c\u307e\u3059\u3002<\/p>\n<p>\u30d9\u30eb\u30cc\u30fc\u30a4\u8a66\u884c\u306b\u3088\u3063\u3066\u78ba\u7387\u306f\u7570\u306a\u308a\u307e\u3059\u3002\u4f8b\u3048\u3070\u30b3\u30a4\u30f3\u3092\u6295\u3052\u308b\u5834\u5408\u3001\u8868\u304c\u51fa\u308b\u78ba\u7387\u306f\\(\\displaystyle\\frac{1}{2}\\)\u3067\u3059\u3002\u307e\u305f\u30b3\u30a4\u30f3\u3092\u6295\u3052\u308b\u3068\u304d\u30011\u306e\u76ee\u304c\u51fa\u308b\u78ba\u7387\u306f\\(\\displaystyle\\frac{1}{6}\\)\u3067\u3059\u3002<\/p>\n<p>\u30d9\u30eb\u30cc\u30fc\u30a4\u8a66\u884c\u306e\u7a2e\u985e\u306b\u3088\u3063\u3066\u78ba\u7387\u304c\u9055\u3046\u306e\u306f\u5f53\u7136\u3067\u3059\u3002\u305f\u3060\u3044\u305a\u308c\u306b\u3057\u3066\u3082\u3001\u30d9\u30eb\u30cc\u30fc\u30a4\u8a66\u884c\u3067\u306f\\(x=0\\)\u306e\u3068\u304d\u3068\\(x=1\\)\u306e\u3068\u304d\u306e2\u3064\u306e\u78ba\u7387\u3092\u5f97\u3089\u308c\u307e\u3059\u3002<\/p>\n<p>\u30b3\u30a4\u30f3\u3092\u6295\u3052\u308b\u5834\u5408\u3001\\(x=0\\)\uff08\u8868\uff09\u306e\u78ba\u7387\u306f\\(\\displaystyle\\frac{1}{2}\\)\u3067\u3042\u308a\u3001\\(x=1\\)\uff08\u88cf\uff09\u306e\u78ba\u7387\u306f\\(\\displaystyle\\frac{1}{2}\\)\u3067\u3059\u3002\u307e\u305f\u30b5\u30a4\u30b3\u30ed\u3092\u6295\u3052\u308b\u5834\u5408\u30011\u306e\u76ee\u304c\u51fa\u308b\u5834\u5408\u3092\u57fa\u6e96\u306b\u3059\u308b\u3068\u3001\\(x=0\\)\uff081\u306e\u76ee\uff09\u306e\u78ba\u7387\u306f\\(\\displaystyle\\frac{1}{6}\\)\u3067\u3059\u3002\u307e\u305f\\(x=1\\)\uff081\u4ee5\u5916\u306e\u76ee\uff09\u306e\u78ba\u7387\u306f\\(\\displaystyle\\frac{5}{6}\\)\u3067\u3059\u30022\u3064\u306e\u7d50\u679c\u306b\u3064\u3044\u3066\u3001\u78ba\u7387\u3092\u8868\u3059\u306e\u304c\u30d9\u30eb\u30cc\u30fc\u30a4\u5206\u5e03\u3067\u3059\u3002<\/p>\n<p>\u306a\u304a\\(x=1\\)\u3068\u306a\u308b\u78ba\u7387\u3092p\u3068\u3059\u308b\u3068\u304d\u3001\\(x=0\\)\u306e\u78ba\u7387\u306f\\(1-p\\)\u3067\u8a08\u7b97\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3059\u3079\u3066\u306e\u78ba\u7387\u3092\u8db3\u3059\u30681\uff08100%\uff09\u306b\u306a\u308b\u305f\u3081\u3001\u3053\u308c\u306b\u3064\u3044\u3066\u306f\u7406\u89e3\u3067\u304d\u308b\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n<h3>\u30d9\u30eb\u30cc\u30fc\u30a4\u5206\u5e03\u3067\u5229\u7528\u3055\u308c\u308b\u516c\u5f0f\uff08\u78ba\u7387\u8cea\u91cf\u95a2\u6570\uff09<\/h3>\n<p>\u524d\u8ff0\u306e\u901a\u308a\\(x=1\\)\uff08\u6210\u529f\uff09\u306e\u3068\u304d\u306e\u78ba\u7387\u304c\\(p\\)\u306e\u5834\u5408\u3001\\(x=0\\)\uff08\u5931\u6557\uff09\u306e\u3068\u304d\u306e\u78ba\u7387\u306f\\(1-p\\)\u3067\u3059\u3002\u3053\u308c\u3092\u96e3\u3057\u304f\u8a18\u8f09\u3059\u308b\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(P(X=1)=p\\)<\/li>\n<li>\\(P(X=0)=1-p\\)<\/li>\n<\/ul>\n<p>\u307e\u305f\u30d9\u30eb\u30cc\u30fc\u30a4\u5206\u5e03\u3067\u5229\u7528\u3055\u308c\u308b\u516c\u5f0f\u3068\u3057\u3066\u3001\u4ee5\u4e0b\u306e\u78ba\u7387\u8cea\u91cf\u95a2\u6570\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<p>\\(P(X=k)=p^k(1-p)^{1-k}\\)<\/p>\n<p>\u203b\\(k=0,1\\)<\/p>\n<p>\u3053\u306e\u516c\u5f0f\u306f\u4f55\u3092\u610f\u5473\u3057\u3066\u3044\u308b\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u78ba\u7387\u8cea\u91cf\u95a2\u6570\u3092\u307f\u308b\u3068\u96e3\u3057\u3044\u6570\u5f0f\u306e\u3088\u3046\u306b\u611f\u3058\u3066\u3057\u307e\u3044\u307e\u3059\u3002\u305f\u3060\u5b9f\u969b\u306b\u306f\u96e3\u3057\u304f\u306a\u304f\u3001\u3053\u308c\u307e\u3067\u8aac\u660e\u3057\u3066\u304d\u305f\u3053\u3068\u3092\u6570\u5f0f\u3067\u8868\u3057\u3066\u3044\u308b\u306b\u3059\u304e\u307e\u305b\u3093\u3002<\/p>\n<p>\u524d\u8ff0\u306e\u901a\u308a\u3001\u30d9\u30eb\u30cc\u30fc\u30a4\u8a66\u884c\u3067\u306f2\u3064\u306e\u7d50\u679c\u306e\u307f\u5f97\u3089\u308c\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u30d9\u30eb\u30cc\u30fc\u30a4\u5206\u5e03\u306b\u306f\\(x=0\\)\u307e\u305f\u306f\\(x=1\\)\u306e2\u3064\u3057\u304b\u3042\u308a\u307e\u305b\u3093\u3002\u305d\u3053\u3067\u3001\u5b9f\u969b\u306b\\(x=0\\)\u307e\u305f\u306f\\(x=1\\)\u3092\u78ba\u7387\u8cea\u91cf\u95a2\u6570\u306b\u4ee3\u5165\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(P(X=0)=p^0(1-p)^{1-0}=1-p\\)<\/p>\n<p>\\(P(X=1)=p^1(1-p)^{1-1}=p\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\\(x=0\\)\u306e\u3068\u304d\u306e\u78ba\u7387\u306f\\(1-p\\)\u3068\u306a\u308a\u3001\\(x=1\\)\u306e\u3068\u304d\u306e\u78ba\u7387\u306f\\(p\\)\u3068\u306a\u308a\u307e\u3059\u3002\u30d9\u30eb\u30cc\u30fc\u30a4\u5206\u5e03\u306e\u516c\u5f0f\u306f\u91cd\u8981\u3067\u306f\u306a\u304f\u3001\u3053\u3053\u307e\u3067\u89e3\u8aac\u3057\u305f\u5358\u7d14\u306a\u3053\u3068\u3092\u7406\u89e3\u3067\u304d\u308c\u3070\u305d\u308c\u3067\u5145\u5206\u3067\u3059\u3002<\/p>\n<h3>\u4e8b\u8c61\u304c\u4e00\u56de\u8d77\u3053\u308b\u78ba\u7387\u304c\u30d9\u30eb\u30cc\u30fc\u30a4\u5206\u5e03\u306e\u671f\u5f85\u5024\u3068\u5206\u6563<\/h3>\n<p>\u305d\u308c\u3067\u306f\u3001\u30d9\u30eb\u30cc\u30fc\u30a4\u5206\u5e03\u306e\u671f\u5f85\u5024\\(E(X)\\)\u306f\u3069\u306e\u3088\u3046\u306b\u8a08\u7b97\u3059\u308c\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u30d9\u30eb\u30cc\u30fc\u30a4\u5206\u5e03\u306f\u30d9\u30eb\u30cc\u30fc\u30a4\u8a66\u884c\u3092\u4e00\u56de\u884c\u3046\u3053\u3068\u306b\u3088\u3063\u3066\u5f97\u3089\u308c\u308b\u5206\u5e03\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u671f\u5f85\u5024\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(E(X)=p\\)<\/li>\n<\/ul>\n<p>\u3064\u307e\u308a\u3001<span style=\"color: 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