{"id":6031,"date":"2022-05-09T22:49:50","date_gmt":"2022-05-09T13:49:50","guid":{"rendered":"https:\/\/hatsudy.com\/jp\/?p=6031"},"modified":"2022-05-28T22:26:48","modified_gmt":"2022-05-28T13:26:48","slug":"geometric-distribution","status":"publish","type":"post","link":"https:\/\/hatsudy.com\/jp\/geometric-distribution.html","title":{"rendered":"\u5e7e\u4f55\u5206\u5e03\uff1a\u5206\u5e03\u306e\u6982\u5ff5\u3084\u671f\u5f85\u5024\u30fb\u5206\u6563\u306e\u8a08\u7b97\u3001\u7121\u8a18\u61b6\u6027\u306e\u610f\u5473"},"content":{"rendered":"\n<p>\u7d71\u8a08\u5b66\u3067\u6700\u3082\u91cd\u8981\u306a\u5206\u5e03\u304c\u6b63\u898f\u5206\u5e03\u3067\u3059\u3002\u305f\u3060\u7d71\u8a08\u3067\u306f\u591a\u304f\u306e\u5206\u5e03\u306e\u7a2e\u985e\u304c\u3042\u308a\u3001\u305d\u306e\u4e00\u3064\u304c\u5e7e\u4f55\u5206\u5e03\u3067\u3059\u3002\u5e7e\u4f55\u5206\u5e03\u306f\u6b63\u898f\u5206\u5e03\u306e\u3088\u3046\u306b\u91cd\u8981\u306a\u5206\u91ce\u3067\u306f\u306a\u3044\u3082\u306e\u306e\u3001\u7d71\u8a08\u3092\u5b66\u3076\u3068\u304d\u306b\u5e7e\u4f55\u5206\u5e03\u3092\u52c9\u5f37\u3057\u306a\u3051\u308c\u3070\u3044\u3051\u306a\u3044\u30b1\u30fc\u30b9\u306f\u591a\u3044\u3067\u3059\u3002<\/p>\n<p>\u9ad8\u6821\u6570\u5b66\u3067\u78ba\u7387\u3084\u7b49\u6bd4\u6570\u5217\u3092\u7406\u89e3\u3057\u3066\u3044\u308b\u5834\u5408\u3001\u5e7e\u4f55\u5206\u5e03\u304c\u4f55\u3092\u610f\u5473\u3057\u3066\u3044\u308b\u306e\u304b\u308f\u304b\u308a\u307e\u3059\u3002\u6982\u5ff5\u306f\u96e3\u3057\u304f\u306a\u3044\u3082\u306e\u306e\u3001\u671f\u5f85\u5024\u3084\u5206\u6563\u306e\u8a08\u7b97\u3092\u3059\u308b\u305f\u3081\u306b\u306f\u78ba\u7387\u3092\u7406\u89e3\u3057\u306a\u3051\u308c\u3070\u3044\u3051\u307e\u305b\u3093\u3002<\/p>\n<p>\u307e\u305f\u3001\u5e7e\u4f55\u5206\u5e03\u306b\u306f\u7121\u8a18\u61b6\u6027\u3068\u3044\u3046\u6027\u8cea\u304c\u3042\u308a\u307e\u3059\u3002\u96e2\u6563\u578b\u78ba\u7387\u5206\u5e03\u306e\u4e2d\u3067\u3082\u3001\u5e7e\u4f55\u5206\u5e03\u306b\u7279\u6709\u306e\u6027\u8cea\u304c\u7121\u8a18\u61b6\u6027\u3067\u3059\u3002\u305d\u3053\u3067\u3001\u7121\u8a18\u61b6\u6027\u304c\u4f55\u3092\u610f\u5473\u3057\u3066\u3044\u308b\u306e\u304b\u7406\u89e3\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u9ad8\u6821\u6570\u5b66\u306e\u77e5\u8b58\u304c\u3042\u308c\u3070\u5e7e\u4f55\u5206\u5e03\u3092\u7406\u89e3\u3067\u304d\u307e\u3059\u3002\u305d\u3053\u3067\u5e7e\u4f55\u5206\u5e03\u306e\u6027\u8cea\u3084\u671f\u5f85\u5024\u30fb\u5206\u6563\u306e\u51fa\u3057\u65b9\u3001\u7121\u8a18\u61b6\u6027\u306e\u7279\u5fb4\u3092\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<h2>\u5e7e\u4f55\u5206\u5e03\u3067\u306f\u30d9\u30eb\u30cc\u30fc\u30a4\u8a66\u884c\u3092\u5229\u7528\u3057\u3066\u5b9a\u3081\u308b<\/h2>\n<p>\u5e7e\u4f55\u5206\u5e03\u3092\u5b66\u3076\u524d\u306b<span style=\"color: #ff0000;\">\u30d9\u30eb\u30cc\u30fc\u30a4\u8a66\u884c<\/span>\u3092\u7406\u89e3\u3057\u306a\u3051\u308c\u3070\u3044\u3051\u307e\u305b\u3093\u3002\u30d9\u30eb\u30cc\u30fc\u30a4\u8a66\u884c\u3068\u306f\u3001\u300c\u4e8c\u8005\u629e\u4e00\uff08\u7d50\u679c\u304c2\u3064\u306e\u307f\uff09\u3067\u3042\u308a\u3001\u72ec\u7acb\u306a\u8a66\u884c\u300d\u3092\u6307\u3057\u307e\u3059\u3002<\/p>\n<p>\u4f8b\u3048\u3070\u30b3\u30a4\u30f3\u3092\u6295\u3052\u308b\u3068\u304d\u3001\u7d50\u679c\u306f\u8868\u3068\u88cf\u306e\u307f\u3067\u3059\u3002\u307e\u305f\u3001\u78ba\u7387\u306f\u305d\u308c\u305e\u308c\\(\\displaystyle\\frac{1}{2}\\)\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u30b3\u30a4\u30f3\u6295\u3052\u3068\u3044\u3046\u306e\u306f\u3001\u78ba\u7387\u304c\u4e00\u5b9a\u306e\u30d9\u30eb\u30cc\u30fc\u30a4\u8a66\u884c\u3067\u3059\u3002<\/p>\n<p>\u307e\u305f\u30b5\u30a4\u30b3\u30ed\u306b\u3064\u3044\u3066\u3082\u30d9\u30eb\u30cc\u30fc\u30a4\u8a66\u884c\u3067\u3059\u3002\u51fa\u308b\u76ee\u304c1\u306e\u5834\u5408\u3092\u6210\u529f\u3001\u305d\u308c\u4ee5\u5916\u306e\u76ee\u304c\u51fa\u305f\u3089\u5931\u6557\u3068\u3059\u308b\u3068\u3001\u7d50\u679c\u306f2\u3064\u306e\u307f\u3067\u3059\u3002\u307e\u305f\u6210\u529f\u78ba\u7387\u306f\\(\\displaystyle\\frac{1}{6}\\)\u3067\u3042\u308a\u3001\u5931\u6557\u78ba\u7387\u306f\\(\\displaystyle\\frac{5}{6}\\)\u3067\u3059\u3002\u3053\u308c\u304c\u3001\u30b5\u30a4\u30b3\u30ed\u3092\u6295\u3052\u308b\u3068\u304d\u306b\u30d9\u30eb\u30cc\u30fc\u30a4\u8a66\u884c\u3068\u306a\u308b\u7406\u7531\u3067\u3059\u3002<\/p>\n<p>\u5e7e\u4f55\u5206\u5e03\u3067\u306f\u30d9\u30eb\u30cc\u30fc\u30a4\u8a66\u884c\u3092\u5229\u7528\u3057\u307e\u3059\u3002\u307e\u305f<span style=\"color: #0000ff;\">\u5e7e\u4f55\u5206\u5e03\u3068\u3044\u3046\u306e\u306f\u3001\u300c\u521d\u3081\u3066\u6210\u529f\u3059\u308b\u78ba\u7387\u306f\u3044\u304f\u3089\u304b\u300d\u3092\u8868\u3057\u307e\u3059\u3002<\/span>\u4f8b\u3048\u3070\u300c\u30b5\u30a4\u30b3\u30ed\u3092\u6295\u3052\u30011\u306e\u76ee\u304c\u51fa\u308b\u3068\u6210\u529f\u3068\u5224\u5b9a\u3059\u308b\u300d\u3068\u3057\u307e\u3059\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u30b5\u30a4\u30b3\u30ed\u30925\u56de\u6295\u3052\u3001\u3088\u3046\u3084\u304f1\u306e\u76ee\u304c\u51fa\u308b\u5834\u5408\u3001\u78ba\u7387\u306f\u3044\u304f\u3089\u3067\u3057\u3087\u3046\u304b\u30025\u56de\u76ee\u306b\u6210\u529f\u3068\u306a\u308b\u305f\u3081\u30014\u56de\u76ee\u307e\u3067\u306f\u9023\u7d9a\u3057\u30661\u4ee5\u5916\u306e\u76ee\u304c\u51fa\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u30014\u56de\u76ee\u307e\u3067\u5931\u6557\u3059\u308b\u78ba\u7387\uff081\u306e\u76ee\u4ee5\u5916\u304c\u51fa\u308b\u78ba\u7387\uff09\u306f\\(\\left(\\displaystyle\\frac{5}{6}\\right)^4\\)\u3067\u3059\u3002<\/p>\n<p>4\u56de\u76ee\u307e\u3067\u5931\u6557\u3057\u305f\u5f8c\u30015\u56de\u76ee\u306b1\u306e\u76ee\u304c\u51fa\u308b\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u5f0f\u306b\u3088\u3063\u3066\u78ba\u7387\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\\(\\left(\\displaystyle\\frac{5}{6}\\right)^4\u00d7\\displaystyle\\frac{1}{6}\\)<\/p>\n<p>\u3053\u306e\u3088\u3046\u306b<span style=\"color: #ff0000;\">\u5e7e\u4f55\u5206\u5e03\u3067\u306f\u3001\u5931\u6557\u78ba\u7387\u3068\u5931\u6557\u56de\u6570\u3092\u5229\u7528\u3057\u3066\u5f0f\u3092\u4f5c\u3063\u305f\u5f8c\u3001\u6210\u529f\u78ba\u7387\u3092\u304b\u3051\u307e\u3059\u3002<\/span><\/p>\n<p>\u6b21\u306b\u3001\u3053\u308c\u3092\u6570\u5f0f\u3067\u8868\u3057\u307e\u3057\u3087\u3046\u3002\u6210\u529f\u78ba\u7387\u3092p\u3068\u3059\u308b\u3068\u3001\u5931\u6557\u78ba\u7387\u306f\\(1-p\\)\u3067\u3059\u3002\u307e\u305f\u6210\u529f\u3059\u308b\u307e\u3067\u306e\u8a66\u884c\u56de\u6570\u3092\\(k\\)\u3068\u3059\u308b\u3068\u3001\u9023\u7d9a\u3057\u3066\u5931\u6557\u3059\u308b\u56de\u6570\u306f\\(k-1\\)\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u5e7e\u4f55\u5206\u5e03\u3067\u306e\u78ba\u7387\\(P(X=k)\\)\u306f\u4ee5\u4e0b\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(P(X=k)=(1-p)^{k-1}\u00d7p\\)<\/li>\n<\/ul>\n<p>\u5e7e\u4f55\u5206\u5e03\u306e\u78ba\u7387\u304c\u300c\\(k\\)\u56de\u76ee\u306b\u6210\u529f\u3059\u308b\u78ba\u7387\u300d\u3067\u3042\u308b\u3053\u3068\u3092\u7406\u89e3\u3059\u308c\u3070\u3001\u306a\u305c\u3053\u306e\u516c\u5f0f\u306b\u3088\u3063\u3066\u8a08\u7b97\u3067\u304d\u308b\u306e\u304b\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<h3>\u5e7e\u4f55\u5206\u5e03\u306e\u30b0\u30e9\u30d5\u306e\u5f62\u3092\u7406\u89e3\u3059\u308b<\/h3>\n<p>\u305d\u308c\u3067\u306f\u3001\u5e7e\u4f55\u5206\u5e03\u306e\u30b0\u30e9\u30d5\u306f\u3069\u306e\u3088\u3046\u306a\u5f62\u306b\u306a\u308b\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u5b9f\u969b\u306b\u30b0\u30e9\u30d5\u3092\u4f5c\u3063\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u30b3\u30a4\u30f3\u3092\u6295\u3052\u308b\u5834\u5408\u3001\u8868\u3068\u88cf\u306e\u78ba\u7387\u306f\u305d\u308c\u305e\u308c\\(\\displaystyle\\frac{1}{2}\\)\u3067\u3059\u3002\u30b3\u30a4\u30f3\u3092\u6295\u3052\u3066\u8868\u304c\u51fa\u308b\u3068\u304d\u3092\u6210\u529f\u3068\u3059\u308b\u3068\u3001\u5e7e\u4f55\u5206\u5e03\uff08\u521d\u3081\u3066\u8868\u304c\u51fa\u308b\u78ba\u7387\uff09\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>1\u56de\u76ee\uff1a\\(\\displaystyle\\frac{1}{2}\\)<\/li>\n<li>2\u56de\u76ee\uff1a\\(\\displaystyle\\frac{1}{2}\u00d7\\displaystyle\\frac{1}{2}=\\displaystyle\\frac{1}{4}\\)<\/li>\n<li>3\u56de\u76ee\uff1a\\(\\left(\\displaystyle\\frac{1}{2}\\right)^2\u00d7\\displaystyle\\frac{1}{2}=\\displaystyle\\frac{1}{8}\\)<\/li>\n<li>4\u56de\u76ee\uff1a\\(\\left(\\displaystyle\\frac{1}{2}\\right)^3\u00d7\\displaystyle\\frac{1}{2}=\\displaystyle\\frac{1}{16}\\)<\/li>\n<li>5\u56de\u76ee\uff1a\\(\\left(\\displaystyle\\frac{1}{2}\\right)^4\u00d7\\displaystyle\\frac{1}{2}=\\displaystyle\\frac{1}{32}\\)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/05\/jfhw6.jpg\" alt=\"\" width=\"400\" height=\"265\" class=\"aligncenter size-full wp-image-6169\" \/><\/p>\n<p>\u3053\u306e\u3088\u3046\u306b\u3001<span style=\"color: #0000ff;\">\u5e7e\u4f55\u5206\u5e03\u3067\u306f\u8a66\u884c\u56de\u6570\\(k\\)\u304c\u591a\u304f\u306a\u308b\u306b\u5f93\u3063\u3066\u78ba\u7387\u304c\u6e1b\u5c11\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/span>\u3059\u3079\u3066\u306e\u5e7e\u4f55\u5206\u5e03\u306b\u3064\u3044\u3066\u3001\u3053\u306e\u3088\u3046\u306a\u30b0\u30e9\u30d5\u306e\u5f62\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u5f53\u7136\u306a\u304c\u3089\u3001\u8a66\u884c\u56de\u6570\u304c\u591a\u3044\u307b\u3069\u9023\u7d9a\u3057\u3066\u5931\u6557\u3059\u308b\u78ba\u7387\u306f\u4f4e\u304f\u306a\u308a\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u8a66\u884c\u56de\u6570\u304c\u591a\u304f\u306a\u308b\u3068\u3001\u5e7e\u4f55\u5206\u5e03\u306e\u78ba\u7387\u304c\u6e1b\u5c11\u3059\u308b\u306e\u306f\u7406\u89e3\u3067\u304d\u308b\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n<h3>\u9023\u7d9a\u3057\u3066\u5931\u6557\u3059\u308b\u78ba\u7387\u3092\u5e7e\u4f55\u5206\u5e03\u3068\u547c\u3076\u30b1\u30fc\u30b9\u3082\u3042\u308b<\/h3>\n<p>\u306a\u304a\u3001\u5e7e\u4f55\u5206\u5e03\u306b\u306f2\u3064\u306e\u5b9a\u7fa9\u304c\u3042\u308a\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u6559\u79d1\u66f8\u3084\u4eba\u306b\u3088\u3063\u3066\u8aac\u660e\u304c\u7570\u306a\u308a\u3001\u6df7\u4e71\u3059\u308b\u4eba\u304c\u3044\u308b\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u3002\u305f\u3060\u5b9a\u7fa9\u304c2\u3064\u3042\u308b\u305f\u3081\u3001\u4e21\u65b9\u3068\u3082\u6b63\u89e3\u3067\u3059\u3002<\/p>\n<p>\u3053\u3053\u307e\u3067\u306e\u8aac\u660e\u3067\u306f\u3001\u300c\\(k\\)\u56de\u76ee\u306b\u6210\u529f\u3059\u308b\u3068\u304d\u306e\u78ba\u7387\u300d\u3092\u5e7e\u4f55\u5206\u5e03\u3068\u89e3\u8aac\u3057\u3066\u304d\u307e\u3057\u305f\u3002\u4e00\u65b9\u3001\u5e7e\u4f55\u5206\u5e03\u306b\u306f\u300c\u521d\u3081\u3066\u6210\u529f\u3059\u308b\u524d\u306b\u3001\u9023\u7d9a\u3057\u3066\u5931\u6557\u3059\u308b\u78ba\u7387\u300d\u3068\u3044\u3046\u5b9a\u7fa9\u3082\u3042\u308a\u307e\u3059\u3002<\/p>\n<p>\u3053\u306e\u5834\u5408\u3001\u516c\u5f0f\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(P(X=k)=(1-p)^k\u00d7p\\)<\/li>\n<\/ul>\n<p>\u5148\u307b\u3069\u306e\u516c\u5f0f\u306b\u6bd4\u3079\u3066\u3001\\(k\\)\u306e\u5024\u304c1\u3064\u5c11\u306a\u304f\u306a\u308a\u307e\u3059\u3002\u307e\u305f\\((k=0,1,2&#8230;)\\)\u3068\u306a\u308a\u3001\\(k\\)\u306e\u5024\u306f0\u304b\u3089\u30b9\u30bf\u30fc\u30c8\u3057\u307e\u3059\u3002\u3053\u3046\u3057\u305f\u6027\u8cea\u304c\u3042\u308b\u305f\u3081\u3001\u300c\\(k\\)\u56de\u76ee\u306b\u6210\u529f\u3059\u308b\u3068\u304d\u306e\u78ba\u7387\u300d\u3092\u5b9a\u7fa9\u306b\u3059\u308b\u5834\u5408\u306b\u6bd4\u3079\u3066\u6df7\u4e71\u3057\u3084\u3059\u3044\u3067\u3059\u3002<\/p>\n<p>\u3044\u305a\u308c\u306b\u3057\u3066\u3082\u6559\u79d1\u66f8\u306b\u3088\u3063\u3066\u306f\u3001\u300c\u521d\u3081\u3066\u6210\u529f\u3059\u308b\u524d\u306b\u3001\u9023\u7d9a\u3057\u3066\u5931\u6557\u3059\u308b\u78ba\u7387\u300d\u304c\u5b9a\u7fa9\u3068\u306a\u3063\u3066\u3044\u308b\u30b1\u30fc\u30b9\u304c\u3042\u308b\u3053\u3068\u3092\u7406\u89e3\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<h3>\u5e7e\u4f55\u5206\u5e03\u306e\u78ba\u7387\u95a2\u6570\u306e\u548c\uff08\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\uff09\u306f\u7b49\u6bd4\u6570\u5217\u3068\u306a\u308b<\/h3>\n<p>\u6b21\u306b\u3001\u5e7e\u4f55\u5206\u5e03\u306e\u78ba\u7387\u95a2\u6570\u306e\u548c\u3092\u6c42\u3081\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u78ba\u7387\u3092\u3059\u3079\u3066\u8db3\u3059\u3068\u304d\u3001\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\\(F(x)\\)\u3092\u5229\u7528\u3057\u307e\u3059\u3002\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\u3068\u306f\u3001\u8981\u306f\u300c\u3059\u3079\u3066\u306e\u78ba\u7387\u3092\u8db3\u3059\u3053\u3068\u300d\u3092\u6307\u3057\u307e\u3059\u3002<\/p>\n<p>\u305d\u3053\u3067\u5148\u307b\u3069\u89e3\u8aac\u3057\u305f\u4ee5\u4e0b\u306e\u516c\u5f0f\u306b\u3064\u3044\u3066\u3001\u3059\u3079\u3066\u8db3\u3059\u5834\u5408\u3092\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\(P(X=k)=(1-p)^{k-1}\u00d7p\\)<\/li>\n<\/ul>\n<p>\u3059\u3079\u3066\u306e\u78ba\u7387\u3092\u8db3\u3059\u5834\u5408\u3001\u4ee5\u4e0b\u306e\u8a08\u7b97\u5f0f\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\\(p+p(1-p)+p(1-p)^2\\)\\(+&#8230;\\)\\(+p(1-p)^{n-1}\\)<\/p>\n<p>\\(=\\displaystyle\\sum_{k=1}^{n}{p(1-p)^{k-1}}\\)<\/p>\n<p>\u3053\u308c\u306f\u3064\u307e\u308a\u3001<span style=\"color: #ff0000;\">\u521d\u9805p\u3001<\/span><span><span style=\"color: #ff0000;\">\u516c\u6bd4\\((1-p)\\)\u306e\u7b49\u6bd4\u6570\u5217\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/span>\u7b49\u6bd4\u6570\u5217\u3092\u3059\u3079\u3066\u8db3\u3059\u5834\u5408\u3001\u4ee5\u4e0b\u306e\u516c\u5f0f\u306b\u306a\u308a\u307e\u3059\u3002<\/span><\/p>\n<p>\\(\\displaystyle\\sum_{k=1}^{n}{ar^{k-1}}=\\displaystyle\\frac{a(1-r^n)}{1-r}\\)<\/p>\n<p>\u203b\\(a\\)\u306f\u521d\u9805\u3001\\(r\\)\u306f\u516c\u6bd4<\/p>\n<p>\u7b49\u6bd4\u6570\u5217\u306e\u548c\u306e\u516c\u5f0f\u3092\u5229\u7528\u3059\u308b\u3068\u3001\u5e7e\u4f55\u5206\u5e03\u3067\u306e\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\\(F(x)\\)\u3092\u5c0e\u304d\u51fa\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u307e\u305f\u3001\u3059\u3079\u3066\u306e\u78ba\u7387\u3092\u8db3\u3059\u5834\u5408\u306e\u8a08\u7b97\u5f0f\u306f\u4ee5\u4e0b\u3067\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/05\/jfwj12.jpg\" alt=\"\" width=\"600\" height=\"195\" class=\"aligncenter size-full wp-image-6197\" \/><\/p>\n<p>\u5f53\u7136\u3067\u306f\u3042\u308a\u307e\u3059\u304c\u3001\u3059\u3079\u3066\u306e\u78ba\u7387\u3092\u8db3\u3059\u30681\uff08100%\uff09\u306b\u306a\u308a\u307e\u3059\u3002\u3053\u3053\u307e\u3067\u306e\u89e3\u8aac\u3067\u91cd\u8981\u306a\u306e\u306f\u3001\u5e7e\u4f55\u5206\u5e03\u306e\u78ba\u7387\u3092\u8db3\u3059\u3068\u304d\u306f\u7b49\u6bd4\u6570\u5217\u306b\u306a\u308b\u3053\u3068\u3067\u3059\u3002<\/p>\n<h2>\u78ba\u7387P\u306e\u5e7e\u4f55\u5206\u5e03\u306b\u3064\u3044\u3066\u3001\u671f\u5f85\u5024\uff08\u5e73\u5747\uff09\u3092\u8a08\u7b97\u3059\u308b<\/h2>\n<p>\u305d\u308c\u3067\u306f\u3001\u5e7e\u4f55\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\u5e7e\u4f55\u5206\u5e03\u3067\u671f\u5f85\u5024\uff08\u5e73\u5747\uff09\u3092\u5f97\u308b\u516c\u5f0f\u306f\u4ee5\u4e0b\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(E(X)=\\displaystyle\\frac{1}{p}\\)<\/li>\n<\/ul>\n<p>\u3053\u306e\u516c\u5f0f\u3092\u5c0e\u304d\u51fa\u3057\u307e\u3057\u3087\u3046\u3002\u307e\u305a\u3001\u671f\u5f85\u5024\\(E(X)\\)\u306f\u305d\u308c\u305e\u308c\u306e\u78ba\u7387\u5909\u6570\u3068\u671f\u5f85\u5024\u3092\u304b\u3051\u305f\u5f8c\u3001\u3059\u3079\u3066\u8db3\u3059\u3053\u3068\u306b\u3088\u3063\u3066\u5f97\u3089\u308c\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u671f\u5f85\u5024\\(=X_1P_1+X_2P_2+&#8230;+X_nP_n\\)<\/li>\n<li>\u671f\u5f85\u5024\\(=\\displaystyle \\sum_{k=1}^n X_kP_k\\)<\/li>\n<\/ul>\n<p>\u5e7e\u4f55\u5206\u5e03\u3067\u306f\u78ba\u7387\u5909\u6570\\(k\\)\u3001\u78ba\u7387P\u306f\\(p(1-p)^{k-1}\\)\u3067\u3059\u3002\u305d\u3053\u3067\u3001\u7121\u9650\u5927\uff08\u221e\uff09\u307e\u3067\u8db3\u3059\u3068\u304d\u306e\u671f\u5f85\u5024\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\\(E(X)=p(1-p)^0\\)\\(+2p(1-p)^1\\)\\(+3p(1-p)^2\\)\\(&#8230;\\)<\/p>\n<p>\\(=\\displaystyle \\sum_{k=1}^\u221e kp(1-p)^{k-1}\\)<\/p>\n<p>\\(=p\\displaystyle \\sum_{k=1}^\u221e k(1-p)^{k-1}\\)<\/p>\n<p>\u3053\u3053\u3067\u3001\\(m=\\displaystyle \\sum_{k=1}^\u221e k(1-p)^{k-1}\\)\u3068\u3057\u307e\u3057\u3087\u3046\u3002\u3064\u307e\u308a\u3001\\(E(X)=pm\\)\u3067\u3059\u3002\u307e\u305f\u3001\\(m\\)\u306e\u4e21\u8fba\u306b\\((1-p)\\)\u3092\u304b\u3051\u305f\u5f8c\u3001\\(m\\)\u304b\u3089\u5f15\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/05\/jfhw8.jpg\" alt=\"\" width=\"600\" height=\"214\" class=\"aligncenter size-full wp-image-6174\" \/><\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\\(E(X)=pm\\)\u306f\u521d\u98051\u3001\u516c\u6bd4\\((1-p)\\)\u306e\u7b49\u6bd4\u6570\u5217\u3067\u3042\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u7b49\u6bd4\u6570\u5217\u306e\u548c\u306e\u516c\u5f0f\u3092\u5229\u7528\u3057\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u671f\u5f85\u5024\uff08\u5e73\u5747\uff09\u306e\u516c\u5f0f\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\\(E(X)=\\displaystyle\\frac{1}{1-(1-p)}\\)<\/p>\n<p>\\(E(X)=\\displaystyle\\frac{1}{p}\\)<\/p>\n<p>\u306a\u304a\u78ba\u7387\\((1-p)\\)\u306f1\u3088\u308a\u3082\u5c0f\u3055\u3044\u5024\u3067\u3059\u3002\u307e\u305f\\(k=n=\u221e\\)\uff08\u7121\u9650\u5927\uff09\u3067\u3042\u308a\u3001\\(n\\)\u306e\u5024\u3092\u6975\u9650\u307e\u3067\u5927\u304d\u304f\u3057\u3066\u3044\u304f\u3068\u3001\u5148\u307b\u3069\u306e\u56f3\u3067\u89e3\u8aac\u3057\u305f\u901a\u308a\\((1-p)^n=0\\)\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u5e7e\u4f55\u5206\u5e03\u3067\u306e\u671f\u5f85\u5024\\(E(X)\\)\u306e\u516c\u5f0f\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<h3>\u5e7e\u4f55\u5206\u5e03\u306e\u5206\u6563\uff08\u6a19\u6e96\u504f\u5dee\uff09\u306e\u51fa\u3057\u65b9<\/h3>\n<p>\u6b21\u306b\u5206\u6563\uff08\u6a19\u6e96\u504f\u5dee\uff09\u3092\u5f97\u308b\u516c\u5f0f\u3092\u51fa\u3057\u307e\u3057\u3087\u3046\u3002\u5e7e\u4f55\u5206\u5e03\u3067\u306e\u5206\u6563\\(V(X)\\)\u306f\u4ee5\u4e0b\u306e\u516c\u5f0f\u306b\u3088\u3063\u3066\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\\(V(X)=\\displaystyle\\frac{1-p}{p^2}\\)<\/p>\n<p>\u307e\u305a\u3001\u5206\u6563\\(V(X)\\)\u306f\u4ee5\u4e0b\u306e\u516c\u5f0f\u306b\u3088\u3063\u3066\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3068\u591a\u304f\u306e\u4eba\u304c\u65e2\u306b\u5b66\u3093\u3067\u3044\u308b\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(V(X)=E(X^2)-E(X)^2\\)<\/li>\n<\/ul>\n<p>\u671f\u5f85\u5024\u306e\u5b9a\u7fa9\u3092\u5229\u7528\u3057\u3066\u300c\u5e7e\u4f55\u5206\u5e03\u3067\u306e\u671f\u5f85\u5024\u3092\u51fa\u3059\u516c\u5f0f\u300d\u3092\u5f97\u305f\u306e\u3068\u540c\u3058\u3088\u3046\u306b\u3001\u5206\u6563\u306e\u5b9a\u7fa9\u3092\u5229\u7528\u3057\u3066\u5e7e\u4f55\u5206\u5e03\u3067\u306e\u5206\u6563\u3092\u51fa\u3059\u516c\u5f0f\u3092\u5f97\u307e\u3057\u3087\u3046\u3002<\/p>\n<p><strong>\u30fb\\(E(X^2)\\)\u306e\u8a08\u7b97<\/strong><\/p>\n<p>\u307e\u305a\u3001\\(E(X^2)\\)\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002\\(E(X)\\)\\(=\\displaystyle \\sum_{k=1}^\u221e kp(1-p)^{k-1}\\)\u3067\u3042\u308b\u305f\u3081\u3001\\(E(X^2)\\)\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\\(E(X^2)=\\displaystyle \\sum_{k=1}^\u221e k^2p(1-p)^{k-1}\\)<\/p>\n<p>\\(=p\\displaystyle \\sum_{k=1}^\u221e k^2(1-p)^{k-1}\\)<\/p>\n<p>\u6b21\u306b\u3001\\(s=\\displaystyle \\sum_{k=1}^\u221e k^2(1-p)^{k-1}\\)\u3068\u3057\u307e\u3057\u3087\u3046\u3002\u3064\u307e\u308a\u3001\\(E(X^2)=ps\\)\u3067\u3059\u3002\u307e\u305f\\((1-p)\\)\u3092\u4e21\u8fba\u306b\u304b\u3051\u3001\\(s\\)\u304b\u3089\u5f15\u304f\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/05\/jfwj1.jpg\" alt=\"\" width=\"600\" height=\"210\" class=\"aligncenter size-full wp-image-6179\" \/><\/p>\n<p>\u3053\u306e\u3088\u3046\u306b\u5f0f\u3092\u5909\u5f62\u3059\u308b\u3068\u3001\\(E(X^2)\\)\u306f\u7b49\u5dee\u6570\u5217\\((2k-1)\\)\u3068\u7b49\u6bd4\u6570\u5217\\((1-p)^{k-1}\\)\u306e\u304b\u3051\u7b97\u3067\u3042\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/05\/jfwj2.jpg\" alt=\"\" width=\"600\" height=\"430\" class=\"aligncenter size-full wp-image-6180\" \/><\/p>\n<p>\u306a\u304a\u671f\u5f85\u5024\u306e\u516c\u5f0f\u3092\u5f97\u308b\u3068\u304d\u3001\\(E(X)\\)\\(=mp\\)\\(=\\displaystyle\\frac{1}{p}\\)\u3067\u3042\u308b\u3053\u3068\u3092\u89e3\u8aac\u3057\u307e\u3057\u305f\u3002\u3064\u307e\u308a\u3001\\(m=\\displaystyle\\frac{1}{p^2}\\)\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001\\(2m\\)\u306f\\(\\displaystyle\\frac{2}{p^2}\\)\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u307e\u305f\u5f0f\u306e\u53f3\u5074\u306b\u3064\u3044\u3066\u3001\u521d\u98051\u3001\u516c\u6bd4\\((1-p)\\)\u306e\u7121\u9650\u7b49\u6bd4\u7d1a\u6570\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u548c\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\\(\\displaystyle\\sum_{k=1}^{\u221e}{(1-p)^{k-1}}\\)<\/p>\n<p>\\(=\\displaystyle\\frac{1}{1-(1-p)}\\)<\/p>\n<p>\\(=\\displaystyle\\frac{1}{p}\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\\(E(X^2)\\)\u306f\u4ee5\u4e0b\u306b\u306a\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<p>\\(E(X^2)=\\displaystyle\\frac{2}{p^2}-\\displaystyle\\frac{1}{p}\\)\\(=\\displaystyle\\frac{2-p}{p^2}\\)<\/p>\n<p>\u306a\u304a\u671f\u5f85\u5024\u306f\\(E(X)=\\displaystyle\\frac{1}{p}\\)\u3068\u308f\u304b\u3063\u3066\u3044\u308b\u305f\u3081\u3001\\(E(X)^2=\\displaystyle\\frac{1}{p^2}\\)\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\\(V(X)=E(X^2)-E(X)^2\\)<\/p>\n<p>\\(=\\displaystyle\\frac{2-p}{p^2}-\\displaystyle\\frac{1}{p^2}\\)<\/p>\n<p>\\(=\\displaystyle\\frac{1-p}{p^2}\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u5e7e\u4f55\u5206\u5e03\u3067\u306e\u5206\u6563\u306e\u516c\u5f0f\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002\u306a\u304a\u5e7e\u4f55\u5206\u5e03\u306e\u6a19\u6e96\u504f\u5dee\u3092\u5f97\u305f\u3044\u5834\u5408\u3001\u5e73\u65b9\u6839\u3092\u5229\u7528\u3057\u3066\u6a19\u6e96\u504f\u5dee\u3092\u51fa\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<h2>\u5e7e\u4f55\u5206\u5e03\u306e\u7121\u8a18\u61b6\u6027\u3068\u306f\u4f55\u304b<\/h2>\n<p>\u305d\u308c\u3067\u306f\u3001\u5e7e\u4f55\u5206\u5e03\u306b\u7279\u6709\u306e\u7279\u5fb4\u3092\u7406\u89e3\u3057\u307e\u3057\u3087\u3046\u3002\u5e7e\u4f55\u5206\u5e03\u306b\u306f<span style=\"color: #ff0000;\">\u7121\u8a18\u61b6\u6027<\/span>\u304c\u3042\u308a\u307e\u3059\u3002\u7121\u8a18\u61b6\u6027\u3068\u306f\u4f55\u306a\u306e\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<p>\u7121\u8a18\u61b6\u6027\u3068\u306f\u3001\u904e\u53bb\u306e\u30a4\u30d9\u30f3\u30c8\u304c\u5c06\u6765\u306b\u5f71\u97ff\u3092\u4e0e\u3048\u306a\u3044\u3053\u3068\u3092\u610f\u5473\u3057\u3066\u3044\u307e\u3059\u3002\u5e7e\u4f55\u5206\u5e03\u3067\u306f\u3001\u72ec\u7acb\u306e\u8a66\u884c\u3060\u304b\u3089\u3067\u3059\u3002\u305f\u3060\u3001\u3053\u308c\u306b\u3064\u3044\u3066\u306f\u611f\u899a\u7684\u306b\u7406\u89e3\u3067\u304d\u308b\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n<p>\u4f8b\u3048\u3070\u307b\u304b\u306e\u4eba\u304c\u30b3\u30a4\u30f3\u3092\u6295\u3052\u30015\u56de\u9023\u7d9a\u3067\u88cf\uff08\u5931\u6557\uff09\u3067\u3057\u305f\u3002\u305d\u306e\u5f8c\u3001\u3042\u306a\u305f\u304c\u30b3\u30a4\u30f3\u3092\u6295\u3052\u3066\u8868\uff08\u6210\u529f\uff09\u306b\u306a\u308b\u78ba\u7387\u306f\u3044\u304f\u3089\u3067\u3057\u3087\u3046\u304b\u3002\u5f53\u7136\u3001\u3042\u306a\u305f\u304c\u8868\u3092\u5f97\u308b\u78ba\u7387\u306f\\(\\displaystyle\\frac{1}{2}\\)\u3067\u3042\u308a\u3001\u88cf\u306b\u306a\u308b\u78ba\u7387\u306f\\(\\displaystyle\\frac{1}{2}\\)\u3067\u3059\u3002<\/p>\n<p><span style=\"color: #0000ff;\">\u904e\u53bb\u306b\u305f\u304f\u3055\u3093\u5931\u6557\u3057\u305f\u3068\u3057\u3066\u3082\u3001\u5c06\u6765\u306e\u6210\u529f\u78ba\u7387\u306b\u5f71\u97ff\u3092\u4e0e\u3048\u308b\u3053\u3068\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/span>\u4f8b\u3048\u3070\u5b9d\u304f\u3058\u3067\u4f55\u5ea6\u5916\u308c\u305f\u3068\u3057\u3066\u3082\u3001\u5c06\u6765\u5f53\u305f\u308a\u30af\u30b8\u3092\u5f15\u304f\u78ba\u7387\u304c\u9ad8\u304f\u306a\u308b\u3053\u3068\u306f\u306a\u3044\u306e\u3067\u3059\u3002\u8a66\u884c\u304c\u72ec\u7acb\u306e\u5834\u5408\u3001\u5e7e\u4f55\u5206\u5e03\u306f\u7121\u8a18\u61b6\u6027\u3092\u3082\u3064\u306e\u3067\u3059\u3002<\/p>\n<h3>\u7121\u8a18\u61b6\u6027\u306e\u8a3c\u660e\u3068\u96e2\u6563\u578b\u78ba\u7387\u5206\u5e03\u3068\u306e\u95a2\u4fc2<\/h3>\n<p>\u305d\u308c\u3067\u306f\u3001\u5e7e\u4f55\u5206\u5e03\u306e\u7121\u8a18\u61b6\u6027\u3092\u8a3c\u660e\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002\\(m\\)\u3068\\(n\\)\u3092\u6b63\u306e\u6574\u6570\u3068\u3059\u308b\u3068\u3001\u7121\u8a18\u61b6\u6027\u306f\u4ee5\u4e0b\u306e\u5f0f\u3067\u8868\u3055\u308c\u307e\u3059\u3002<\/p>\n<p>\\(P(X=m+n|X\u2265m)\\)\\(=P(X=n)\\)<\/p>\n<p>\u6050\u3089\u304f\u3001\u3053\u306e\u6570\u5f0f\u3092\u307f\u3066\u3082\u610f\u5473\u3092\u7406\u89e3\u3067\u304d\u306a\u3044\u3068\u601d\u3044\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u3042\u306a\u305f\u304c\u30b3\u30a4\u30f3\u6295\u3052\u3092\u3057\u3066\\(n\\)\u56de\u76ee\u306b\u6210\u529f\u3057\u305f\u3068\u3057\u307e\u3059\u3002\\(P(X=n)\\)\u3068\u3044\u3046\u306e\u306f\u3001\u3042\u306a\u305f\u304c\u30b3\u30a4\u30f3\u3092\u6295\u3052\u3066\\(n\\)\u56de\u76ee\u306b\u521d\u3081\u3066\u6210\u529f\u3059\u308b\u78ba\u7387\u3092\u8868\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n<p>\u305f\u3060\u3001\u3042\u306a\u305f\u304c\u30b3\u30a4\u30f3\u3092\u6295\u3052\u308b\u524d\u3001\u307b\u304b\u306e\u4eba\u304c\u30b3\u30a4\u30f3\u3092\\(m\\)\u56de\u6295\u3052\u3001\u3059\u3079\u3066\u5931\u6557\u3057\u3066\u3044\u305f\u3068\u3057\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u3001\\(P(X=m+n)\\)\u306f\\(m+n\\)\u56de\u76ee\u306b\u521d\u3081\u3066\u6210\u529f\u3059\u308b\u78ba\u7387\u3092\u610f\u5473\u3057\u3066\u3044\u307e\u3059\u3002\u307e\u305f\u3001\\(m\\)\u56de\u76ee\u4ee5\u4e0a\u306e\u5931\u6557\u3092\u610f\u5473\u3059\u308b\u306e\u304c\\(X\u2265n\\)\u3067\u3059\u3002<\/p>\n<p>\u307e\u305f\\(P(X=m+n|X\u2265n)\\)\u306f\u6761\u4ef6\u4ed8\u304d\u78ba\u7387\u3067\u3042\u308a\u3001\u300c\\(m\\)\u56de\u76ee\u4ee5\u4e0a\u306e\u5931\u6557\u3092\u9023\u7d9a\u3067\u3059\u308b\u3068\u304d\uff08\\(X\u2265m\\)\u306e\u3068\u304d\uff09\u3001\\(m+n\\)\u56de\u76ee\u306b\u6210\u529f\u3059\u308b\u78ba\u7387\\(P(X=m+n)\\)\u300d\u3092\u8868\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/05\/jfwj6.jpg\" alt=\"\" width=\"500\" height=\"268\" class=\"aligncenter size-full wp-image-6189\" \/><\/p>\n<p><span style=\"color: #0000ff;\">\\(n\\)\u56de\u76ee\u306b\u6210\u529f\u3059\u308b\u78ba\u7387\u304c\\(m+n\\)\u56de\u76ee\u306b\u6210\u529f\u3059\u308b\u78ba\u7387\u3068\u7b49\u3057\u3044\u5834\u5408\u3001\u305d\u308c\u307e\u3067\u306e\\(m\\)\u56de\u306e\u9023\u7d9a\u5931\u6557\u306f\u78ba\u7387\u306b\u5f71\u97ff\u3057\u306a\u3044\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002<\/span>\u6570\u5f0f\u3067\u8868\u3059\u3068\u7406\u89e3\u306f\u96e3\u3057\u3044\u3067\u3059\u304c\u3001\u3053\u306e\u5f0f\u306b\u306f\u3053\u306e\u3088\u3046\u306a\u610f\u5473\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<p>\u306a\u304a\u6761\u4ef6\u4ed8\u304d\u78ba\u7387\u3092\u5b66\u3076\u3068\u304d\u3001\u4ee5\u4e0b\u306e\u516c\u5f0f\u3092\u65e2\u306b\u7fd2\u3063\u3066\u3044\u308b\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n<p>\\(P(A|B)=\\displaystyle\\frac{A\u2229B}{B}\\)<\/p>\n<p>\u305d\u3053\u3067\u3001\u3053\u306e\u516c\u5f0f\u3092\u5229\u7528\u3057\u3066\u7121\u8a18\u61b6\u6027\u306e\u8a3c\u660e\u3092\u3057\u307e\u3057\u3087\u3046\u3002\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\\(P(X=m+n|X\u2265m)\\)\\(=\\displaystyle\\frac{P((X=m+n)\u2229(X\u2265m))}{P(X\u2265m)}\\)<\/p>\n<p>\u306a\u304am\u56de\u4ee5\u4e0a\u9023\u7d9a\u3067\u5931\u6557\u3057\u3001\u304b\u3064\\(m+n\\)\u56de\u76ee\u3067\u6210\u529f\u3059\u308b\u78ba\u7387\u3068\u3044\u3046\u306e\u306f\u3001\u8981\u306f\\(m+n\\)\u56de\u76ee\u3067\u521d\u3081\u3066\u6210\u529f\u3059\u308b\u78ba\u7387\u3092\u6307\u3057\u307e\u3059\u3002\u3064\u307e\u308a\u3001\\(P((X=m+n)\u2229(X\u2265m))\\)\\(=P(X=m+n)\\)\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\\(\\displaystyle\\frac{P((X=m+n)\u2229(X\u2265m))}{P(X\u2265m)}\\)<\/p>\n<p>\\(=\\displaystyle\\frac{P(X=m+n)}{P(X\u2265m)}\\)<\/p>\n<p>\u306a\u304a\u5e7e\u4f55\u5206\u5e03\u3067\u78ba\u7387\u3092\u5f97\u308b\u516c\u5f0f\u306f\\(P(X=k)\\)\\(=p(1-p)^{k-1}\\)\u3067\u3042\u308b\u305f\u3081\u3001\\(P(X=m+n)\\)\u306e\u78ba\u7387\u306f\u4ee5\u4e0b\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\\(P(X=m+n)=p(1-p)^{m+n-1}\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u5206\u5b50\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002\u6b21\u306b\u5206\u6bcd\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u3053\u3053\u3067\u306f\\(m\\)\u56de\u9023\u7d9a\u3067\u5931\u6557\u3057\u3001\\(m+1\\)\u56de\u76ee\u306b\u6210\u529f\u3059\u308b\u5834\u9762\u3092\u60f3\u5b9a\u3057\u307e\u3059\u3002\u3053\u306e\u3068\u304d\u306e\u78ba\u7387\u306f\\(P(X=m)\\)\\(=p(1-p)^m\\)\u3067\u3059\u3002\u307e\u305f\\(P(X\u2265m)\\)\u3068\u306f\u3001\u5931\u6557\u304c\\(m\\)\u56de\u4ee5\u4e0a\u3001\u9023\u7d9a\u3057\u3066\u8d77\u3053\u308b\u78ba\u7387\u3067\u3059\u3002\u5931\u6557\u304c\\(m\\)\u56de\u4ee5\u4e0a\u9023\u7d9a\u3059\u308b\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u78ba\u7387\u3092\u8db3\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u5931\u6557\u304c\\(m\\)\u56de\uff1a\\(P(X=m)\\)<\/li>\n<li>\u5931\u6557\u304c\\(m+1\\)\u56de\uff1a\\(P(X=m+1)\\)<\/li>\n<li>\u5931\u6557\u304c\\(m+2\\)\u56de\uff1a\\(P(X=m+2)\\)<\/li>\n<li>&#8230;.<\/li>\n<\/ul>\n<p>\u3053\u308c\u3092\u4f55\u5ea6\u3082\u8db3\u3057\u307e\u3057\u3087\u3046\u3002\u3059\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u8a08\u7b97\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/05\/jfwj8.jpg\" alt=\"\" width=\"700\" height=\"417\" class=\"aligncenter size-full wp-image-6191\" \/><\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\\(P(X\u2265m)=(1-p)^m\\)\u3067\u3042\u308b\u3068\u308f\u304b\u308a\u307e\u3057\u305f\u3002\u305d\u3053\u3067\u3001\\(\\displaystyle\\frac{P(X=m+n)}{P(X\u2265m)}\\)\u3078\u4ee3\u5165\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(\\displaystyle\\frac{P(X=m+n)}{P(X\u2265m)}\\)<\/p>\n<p>\\(=\\displaystyle\\frac{p(1-p)^{m+n-1}}{(1-p)^m}\\)<\/p>\n<p>\\(=p(1-p)^{n-1}\\)<\/p>\n<p>\\(=P(X=n)\\)\uff08\u8a3c\u660e\u5b8c\u4e86\uff09<\/p>\n<p>\u6700\u521d\u306b\u89e3\u8aac\u3057\u305f\u901a\u308a\u3001\u5e7e\u4f55\u5206\u5e03\u306e\u516c\u5f0f\u306f\\(P(X=k)\\)\\(=p(1-p)^{k-1}\\)\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001\\(n\\)\u56de\u76ee\u306b\u521d\u3081\u3066\u6210\u529f\u3059\u308b\u78ba\u7387\u306f\\(P(X=n)\\)\\(=p(1-p)^{n-1}\\)\u3067\u3059\u3002\u3053\u3046\u3057\u3066\u3001\u5e7e\u4f55\u5206\u5e03\u306f\u7121\u8a18\u61b6\u6027\u3092\u3082\u3064\u3053\u3068\u3092\u8a3c\u660e\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<p>\u307e\u305f\u5e7e\u4f55\u5206\u5e03\u306f\u300c\u7d50\u679c\u304c2\u3064\u306e\u30d9\u30eb\u30cc\u30fc\u30a4\u8a66\u884c\u300d\u306b\u57fa\u3065\u3044\u3066\u3044\u308b\u305f\u3081\u3001\u96e2\u6563\u578b\u78ba\u7387\u5206\u5e03\u306b\u306a\u308a\u307e\u3059\u3002<span style=\"color: #0000ff;\">\u96e2\u6563\u578b\u78ba\u7387\u5206\u5e03\u306e\u4e2d\u3067\u3001\u7121\u8a18\u61b6\u6027\u304c\u3042\u308b\u306e\u306f\u5e7e\u4f55\u5206\u5e03\u3060\u3051\u3067\u3059\u3002<\/span>\u305d\u306e\u305f\u3081\u300c\u96e2\u6563\u578b\u78ba\u7387\u5206\u5e03\u3067\u306e\u7121\u8a18\u61b6\u6027\uff1d\u5e7e\u4f55\u5206\u5e03\u300d\u3068\u899a\u3048\u3066\u304a\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n<h2>\u5e7e\u4f55\u5206\u5e03\u306e\u6027\u8cea\u3092\u7406\u89e3\u3057\u3001\u516c\u5f0f\u306e\u610f\u5473\u3092\u5b66\u3076<\/h2>\n<p>\u6b63\u898f\u5206\u5e03\u307b\u3069\u91cd\u8981\u3067\u306f\u306a\u3044\u3082\u306e\u306e\u3001\u7d71\u8a08\u5b66\u3092\u5b66\u3076\u3068\u304d\u306b\u5e7e\u4f55\u5206\u5e03\u3092\u7fd2\u3046\u30b1\u30fc\u30b9\u304c\u3042\u308a\u307e\u3059\u3002\u521d\u3081\u3066\u6210\u529f\u3059\u308b\u78ba\u7387\u304c\u5e7e\u4f55\u5206\u5e03\u3067\u3042\u308b\u3053\u3068\u3092\u7406\u89e3\u3059\u308c\u3070\u3001\u5e7e\u4f55\u5206\u5e03\u306e\u78ba\u7387\u3092\u8a08\u7b97\u3059\u308b\u306e\u306f\u96e3\u3057\u304f\u3042\u308a\u307e\u305b\u3093\u3002<\/p>\n<p>\u305f\u3060\u5e7e\u4f55\u5206\u5e03\u306b\u306f2\u3064\u306e\u5b9a\u7fa9\u304c\u3042\u308b\u306e\u3067\u6df7\u4e71\u3057\u3084\u3059\u3044\u3067\u3059\u3002\u307e\u305f\u671f\u5f85\u5024\u3084\u5206\u6563\u3092\u5f97\u308b\u516c\u5f0f\u3092\u51fa\u3059\u306b\u306f\u3001\u9ad8\u6821\u6570\u5b66\u306e\u8a08\u7b97\u304c\u5fc5\u8981\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u3055\u3089\u306b\u306f\u3001\u5e7e\u4f55\u5206\u5e03\u306b\u306f\u7121\u8a18\u61b6\u6027\u304c\u3042\u308a\u307e\u3059\u3002\u96e2\u6563\u578b\u78ba\u7387\u5206\u5e03\u3067\u7121\u8a18\u61b6\u6027\u3092\u3082\u3064\u306e\u306f\u5e7e\u4f55\u5206\u5e03\u3060\u3051\u3067\u3059\u3002\u305d\u3053\u3067\u3001\u7121\u8a18\u61b6\u6027\u304c\u3069\u306e\u3088\u3046\u306a\u610f\u5473\u3092\u3082\u3064\u306e\u304b\u7406\u89e3\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u5e7e\u4f55\u5206\u5e03\u3092\u5b66\u3076\u3068\u304d\u3001\u671f\u5f85\u5024\u3084\u5206\u6563\u3001\u7121\u8a18\u61b6\u6027\u307e\u3067\u7406\u89e3\u3059\u308b\u5834\u5408\u3001\u96e3\u6613\u5ea6\u304c\u9ad8\u304f\u306a\u308a\u307e\u3059\u3002\u305f\u3060\u9ad8\u6821\u6570\u5b66\u3092\u7406\u89e3\u3057\u3066\u3044\u308c\u3070\u5185\u5bb9\u3092\u628a\u63e1\u3067\u304d\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u305d\u308c\u305e\u308c\u306e\u516c\u5f0f\u304c\u4f55\u3092\u610f\u5473\u3057\u3066\u3044\u308b\u306e\u304b\u3092\u5b66\u3073\u3001\u516c\u5f0f\u306e\u8a3c\u660e\u3092\u542b\u3081\u3066\u7406\u89e3\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u7d71\u8a08\u5b66\u3067\u6700\u3082\u91cd\u8981\u306a\u5206\u5e03\u304c\u6b63\u898f\u5206\u5e03\u3067\u3059\u3002\u305f\u3060\u7d71\u8a08\u3067\u306f\u591a\u304f\u306e\u5206\u5e03\u306e\u7a2e\u985e\u304c\u3042\u308a\u3001\u305d\u306e\u4e00\u3064\u304c\u5e7e\u4f55\u5206\u5e03\u3067\u3059\u3002\u5e7e\u4f55\u5206\u5e03\u306f\u6b63\u898f\u5206\u5e03\u306e\u3088\u3046\u306b\u91cd\u8981\u306a\u5206\u91ce\u3067\u306f\u306a\u3044\u3082\u306e\u306e\u3001\u7d71\u8a08\u3092\u5b66\u3076\u3068\u304d\u306b\u5e7e\u4f55\u5206\u5e03\u3092\u52c9\u5f37\u3057\u306a\u3051\u308c\u3070\u3044\u3051\u306a\u3044\u30b1\u30fc\u30b9\u306f\u591a\u3044\u3067\u3059\u3002 \u9ad8 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