{"id":6434,"date":"2022-05-21T22:02:31","date_gmt":"2022-05-21T13:02:31","guid":{"rendered":"https:\/\/hatsudy.com\/jp\/?p=6434"},"modified":"2023-01-30T02:03:28","modified_gmt":"2023-01-29T17:03:28","slug":"exponential-distribution","status":"publish","type":"post","link":"https:\/\/hatsudy.com\/jp\/exponential-distribution.html","title":{"rendered":"\u6307\u6570\u5206\u5e03\uff1a\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u306e\u610f\u5473\u3084\u671f\u5f85\u5024\uff08\u5e73\u5747\uff09\u30fb\u5206\u6563\u306e\u6c42\u3081\u65b9"},"content":{"rendered":"\n<p>\u7d71\u8a08\u5b66\u3067\u5b66\u3076\u5206\u5e03\u306e\u4e00\u3064\u306b\u6307\u6570\u5206\u5e03\u304c\u3042\u308a\u307e\u3059\u3002\u30e9\u30f3\u30c0\u30e0\u306b\u767a\u751f\u3059\u308b\u30a4\u30d9\u30f3\u30c8\u306b\u5bfe\u3057\u3066\u5229\u7528\u3055\u308c\u308b\u306e\u304c\u6307\u6570\u5206\u5e03\u3067\u3059\u3002<\/p>\n<p>\u30e9\u30f3\u30c0\u30e0\u306a\u30a4\u30d9\u30f3\u30c8\u767a\u751f\u3067\u5229\u7528\u3055\u308c\u308b\u305f\u3081\u3001\u591a\u304f\u306e\u5834\u9762\u3067\u6307\u6570\u5206\u5e03\u306f\u6709\u7528\u3067\u3059\u3002\u5c06\u6765\u306e\u767a\u751f\u78ba\u7387\u3092\u8a08\u7b97\u3059\u308b\u3068\u304d\u3001\u6307\u6570\u5206\u5e03\u3092\u5229\u7528\u3059\u308b\u306e\u3067\u3059\u3002<\/p>\n<p>\u6307\u6570\u5206\u5e03\u306e\u7d2f\u7a4d\u78ba\u7387\u5206\u5e03\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u308c\u3070\u3001\u6642\u9593\u7d4c\u904e\u3068\u5171\u306b\u767a\u751f\u3059\u308b\u30a4\u30d9\u30f3\u30c8\u306e\u78ba\u7387\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u307e\u305f\u516c\u5f0f\u3092\u5229\u7528\u3059\u308c\u3070\u3001\u671f\u5f85\u5024\uff08\u5e73\u5747\uff09\u3084\u5206\u6563\u3092\u5f97\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002\u307b\u304b\u306b\u306f\u3001\u6307\u6570\u5206\u5e03\u306b\u306f\u7121\u8a18\u61b6\u6027\u3068\u3044\u3046\u7279\u5fb4\u3082\u3042\u308a\u307e\u3059\u3002<\/p>\n<p>\u78ba\u7387\u5206\u5e03\u3092\u5b66\u3076\u3068\u304d\u3001\u6307\u6570\u5206\u5e03\u306e\u7279\u5fb4\u3092\u7406\u89e3\u3057\u307e\u3057\u3087\u3046\u3002\u3053\u3053\u3067\u306f\u3001\u6307\u6570\u5206\u5e03\u306e\u5185\u5bb9\u306b\u3064\u3044\u3066\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<h2>\u30e9\u30f3\u30c0\u30e0\u306a\u30a4\u30d9\u30f3\u30c8\u306e\u767a\u751f\u78ba\u7387\u3092\u8868\u3059\u9023\u7d9a\u78ba\u7387\u5206\u5e03<\/h2>\n<p>\u5206\u5e03\u306b\u3088\u3063\u3066\u7279\u5fb4\u304c\u7570\u306a\u308a\u3001\u6307\u6570\u5206\u5e03\u306f\u9023\u7d9a\u578b\u78ba\u7387\u5206\u5e03\u306b\u5206\u985e\u3055\u308c\u307e\u3059\u3002\u307e\u305f\u3001\u30e9\u30f3\u30c0\u30e0\u306a\u30a4\u30d9\u30f3\u30c8\u304c\u767a\u751f\u3059\u308b\u3068\u304d\u306b\u5229\u7528\u3055\u308c\u308b\u78ba\u7387\u5206\u5e03\u3067\u3059\u3002<\/p>\n<p>\u30e9\u30f3\u30c0\u30e0\u306b\u767a\u751f\u3059\u308b\u30a4\u30d9\u30f3\u30c8\u3068\u3057\u3066\u306f\u3001\u4f8b\u3048\u3070\u4ee5\u4e0b\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u5e97\u8217\u3078\u5ba2\u304c\u6765\u308b<\/li>\n<li>\u4ea4\u901a\u4e8b\u6545\u304c\u767a\u751f\u3059\u308b<\/li>\n<li>\u6a5f\u68b0\u304c\u6545\u969c\u3059\u308b<\/li>\n<li>\u5730\u9707\u304c\u767a\u751f\u3059\u308b<\/li>\n<li>\u8857\u4e2d\u3067\u53cb\u4eba\u3068\u3059\u308c\u9055\u3046<\/li>\n<\/ul>\n<p>\u3053\u306e\u3088\u3046\u306b\u3001<span style=\"color: #0000ff;\">\u7a81\u767a\u7684\u306b\u767a\u751f\u3059\u308b\u30a4\u30d9\u30f3\u30c8\u304c\u3069\u308c\u304f\u3089\u3044\u306e\u78ba\u7387\u3067\u8d77\u3053\u308b\u306e\u304b\u63a8\u6e2c\u3067\u304d\u308b\u306e\u304c\u6307\u6570\u5206\u5e03\u3067\u3059\u3002<\/span><\/p>\n<p>\u3053\u3046\u3057\u305f\u30a4\u30d9\u30f3\u30c8\u306f\u5b9a\u671f\u7684\u306b\u767a\u751f\u3057\u3001\u767a\u751f\u78ba\u7387\u306f\u5e38\u306b\u4e00\u5b9a\u3068\u8003\u3048\u307e\u3059\u3002\u6a5f\u68b0\u306f\u3044\u3064\u304b\u58ca\u308c\u307e\u3059\u3057\u3001\u65e5\u672c\u3084\u30a4\u30f3\u30c9\u30cd\u30b7\u30a2\u3067\u306f\u6bce\u5e74\u5730\u9707\u304c\u767a\u751f\u3057\u3066\u3044\u307e\u3059\u3002\u305d\u3046\u3057\u305f\u5834\u5408\u3001\u6307\u6570\u5206\u5e03\u306b\u5f93\u3046\u3068\u3044\u3046\u308f\u3051\u3067\u3059\u3002<\/p>\n<h3>\u30dd\u30a2\u30bd\u30f3\u5206\u5e03\u3068\u6307\u6570\u5206\u5e03\u306e\u9055\u3044\u306f\u4f55\u304b<\/h3>\n<p>\u306a\u304a\u6307\u6570\u5206\u5e03\u306e\u6982\u8981\u3092\u5b66\u3076\u3068\u3001\u591a\u304f\u306e\u4eba\u306f\u300c\u30dd\u30a2\u30bd\u30f3\u5206\u5e03\u3068\u4f55\u304c\u9055\u3046\u306e\u304b\u300d\u3068\u7591\u554f\u306b\u601d\u3044\u307e\u3059\u3002\u30dd\u30a2\u30bd\u30f3\u5206\u5e03\u306b\u3064\u3044\u3066\u3082\u3001\u7a00\u306b\u767a\u751f\u3059\u308b\u30a4\u30d9\u30f3\u30c8\uff08\u7a81\u767a\u7684\u306a\u30a4\u30d9\u30f3\u30c8\uff09\u306e\u78ba\u7387\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u6307\u6570\u5206\u5e03\u3067\u306f\u3001\u6b21\u306e\u30a4\u30d9\u30f3\u30c8\u767a\u751f\u304c\u3044\u3064\u8d77\u3053\u308b\u306e\u304b\u306b\u3064\u3044\u3066\u78ba\u7387\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u4e00\u65b9\u3067\u30dd\u30a2\u30bd\u30f3\u5206\u5e03\u3067\u306f\u3001\u7279\u5b9a\u306e\u6642\u9593\u5185\u306b\u4f55\u56de\u306e\u30a4\u30d9\u30f3\u30c8\u304c\u767a\u751f\u3059\u308b\u306e\u304b\u306b\u3064\u3044\u3066\u78ba\u7387\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u6b21\u306e\u3088\u3046\u306a\u9055\u3044\u304c\u3042\u308b\u3068\u8003\u3048\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\u6307\u6570\u5206\u5e03\uff1a\u6b21\u306e\u767a\u751f\u9593\u9694\u306b\u7740\u76ee\u3059\u308b<\/li>\n<li>\u30dd\u30a2\u30bd\u30f3\u5206\u5e03\uff1a\u7279\u5b9a\u306e\u6642\u9593\u5185\u306b\u767a\u751f\u3059\u308b\u30a4\u30d9\u30f3\u30c8\u56de\u6570\u306b\u7740\u76ee\u3059\u308b<\/li>\n<\/ul>\n<p>\u5b9a\u671f\u7684\u306b\u767a\u751f\u3059\u308b\u30a4\u30d9\u30f3\u30c8\u306b\u5bfe\u3057\u3066\u3001\u6b21\u56de\u30a4\u30d9\u30f3\u30c8\u767a\u751f\u306e\u6642\u9593\u3092\u8abf\u3079\u305f\u3044\u5834\u5408\u306f\u6307\u6570\u5206\u5e03\u3092\u5229\u7528\u3057\u307e\u3059\u3002<\/p>\n<h2>\u6307\u6570\u5206\u5e03\u306e\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u306e\u516c\u5f0f\u3068\u610f\u5473<\/h2>\n<p>\u6b21\u306b\u3001\u6307\u6570\u5206\u5e03\u306e\u516c\u5f0f\u3092\u78ba\u8a8d\u3057\u307e\u3057\u3087\u3046\u3002\u6307\u6570\u5206\u5e03\u306e\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u306f\u4ee5\u4e0b\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(f(x)=\u03bbe^{-\u03bbx}\\)<\/li>\n<\/ul>\n<p>\u6050\u3089\u304f\u610f\u5473\u3092\u7406\u89e3\u3067\u304d\u306a\u3044\u3068\u601d\u3044\u307e\u3059\u304c\u3001\u3072\u3068\u307e\u305a\u3053\u306e\u516c\u5f0f\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u78ba\u7387\u5bc6\u5ea6\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\\(\u03bb\\)\u3068\u3044\u3046\u306e\u306f\u3001\u7279\u5b9a\u306e\u671f\u9593\u306b\u767a\u751f\u3059\u308b\u30a4\u30d9\u30f3\u30c8\u56de\u6570\u3092\u6307\u3057\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u30a4\u30d9\u30f3\u30c8\u306e\u7a2e\u985e\u306b\u3088\u3063\u3066\\(\u03bb\\)\u306f\u7570\u306a\u308a\u307e\u3059\u3002\u4f8b\u3048\u30701\u6642\u9593\u306b\u5e73\u57475\u4eba\u304c\u5165\u5e97\u3059\u308b\u5834\u5408\u30011\u6642\u9593\u3092\u57fa\u6e96\u3068\u3059\u308b\u306a\u3089\\(\u03bb\\)\u306f5\u3067\u3059\u3002\u307e\u305f1\u5e74\u306b2\u56de\u5730\u9707\u304c\u767a\u751f\u3059\u308b\u5834\u5408\u30011\u5e74\u3092\u57fa\u6e96\u306b\u3059\u308b\u306a\u3089\\(\u03bb\\)\u306f2\u3067\u3059\u3002<\/p>\n<p><span style=\"color: #ff0000;\">\u7279\u5b9a\u306e\u671f\u9593\u306b\u5e73\u5747\u3057\u3066\u4f55\u5ea6\u306e\u30a4\u30d9\u30f3\u30c8\u304c\u767a\u751f\u3059\u308b\u306e\u304b\u6570\u3048\u308b\u3053\u3068\u306b\u3088\u3063\u3066\\(\u03bb\\)\u304c\u6c7a\u307e\u308a\u307e\u3059\u3002<\/span><\/p>\n<p>\u307e\u305f\\(x\\)\u306f\u6b21\u306e\u30a4\u30d9\u30f3\u30c8\u304c\u767a\u751f\u3059\u308b\u307e\u3067\u306e\u6642\u9593\u3092\u6307\u3057\u307e\u3059\u3002\u524d\u8ff0\u306e\u901a\u308a\u3001\u6307\u6570\u5206\u5e03\u306f\u6b21\u306e\u767a\u751f\u9593\u9694\u306b\u7740\u76ee\u3057\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u6b21\u306e\u767a\u751f\u6642\u9593\u3068\u3057\u3066\\(x\\)\u3092\u5229\u7528\u3059\u308b\u306e\u3067\u3059\u3002<\/p>\n<p><strong>\u30fb\u5b9f\u969b\u306b\u6307\u6570\u5206\u5e03\u306e\u4f8b\u984c\u3092\u89e3\u3044\u3066\u307f\u308b<\/strong><\/p>\n<p>\u305d\u3053\u3067\u3001\u5b9f\u969b\u306b\u554f\u984c\u3092\u89e3\u3044\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u305d\u3046\u3059\u308c\u3070\u3001\u6307\u6570\u5206\u5e03\u304c\u4f55\u3092\u610f\u5473\u3057\u3066\u3044\u308b\u306e\u304b\u7406\u89e3\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002\u4ee5\u4e0b\u306e\u554f\u984c\u306e\u7b54\u3048\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<ul>\n<li>1\u6642\u9593\u306b\u5e73\u57475\u4eba\u304c\u6765\u5e97\u3059\u308b\u5e97\u8217\u304c\u3042\u308a\u307e\u3059\u300210\u5206\u5f8c\u30d4\u30c3\u30bf\u30ea\u306b\u5ba2\u304c\u6765\u5e97\u3059\u308b\u78ba\u7387\u5bc6\u5ea6\u306f\u3044\u304f\u3089\u3067\u3057\u3087\u3046\u304b\u3002<\/li>\n<\/ul>\n<p>1\u6642\u9593\u306b\u5e73\u57475\u4eba\u304c\u6765\u5e97\u3059\u308b\u305f\u3081\u30011\u6642\u9593\u3092\u57fa\u6e96\u306b\u3059\u308b\u3068\\(\u03bb=5\\)\u3067\u3059\u3002\u307e\u305f\u300110\u5206\u5f8c\u3068\u3044\u3046\u306e\u306f\\(\\displaystyle\\frac{10}{60}\\)\\(=\\displaystyle\\frac{1}{6}\\)\u6642\u9593\u3067\u3059\u3002\u305d\u3053\u3067\u3001\\(x=\\displaystyle\\frac{1}{6}\\)\u3092\u5148\u307b\u3069\u306e\u516c\u5f0f\u306b\u4ee3\u5165\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(f(x)=5e^{-5\u00d7\\displaystyle\\frac{1}{6}}\\)<\/p>\n<p>\\(\u22522.17\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u78ba\u7387\u5bc6\u5ea6\u306f2.17\u306b\u306a\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<h3>\u6307\u6570\u5206\u5e03\u306e\u30b0\u30e9\u30d5\u306f\u3069\u306e\u3088\u3046\u306b\u306a\u3063\u3066\u3044\u308b\u306e\u304b<\/h3>\n<p>\u305d\u308c\u3067\u306f\u3001\u6307\u6570\u5206\u5e03\u306e\u30b0\u30e9\u30d5\u306f\u3069\u306e\u3088\u3046\u306b\u306a\u3063\u3066\u3044\u308b\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u5148\u307b\u3069\u3068\u540c\u3058\u6761\u4ef6\u306b\u3064\u3044\u3066\u3001\\(x\\)\u3092\u5909\u3048\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u3064\u307e\u308a10\u5206\u5f8c\u3060\u3051\u3067\u306a\u304f\u3001\u307b\u304b\u306e\u90e8\u5206\u306e\u78ba\u7387\u5bc6\u5ea6\u306b\u3064\u3044\u3066\u3082\u8a08\u7b97\u3059\u308b\u306e\u3067\u3059\u3002<\/p>\n<p>\u3053\u306e\u5834\u5408\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%; text-align: center; background-color: #fffdd1;\"><strong>\u7d4c\u904e\u6642\u9593<\/strong><\/td>\n<td style=\"width: 50%; text-align: center; background-color: #fffdd1;\"><strong>\u78ba\u7387\u5bc6\u5ea6<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%; text-align: center;\">5\u5206\u5f8c<\/td>\n<td style=\"width: 50%; text-align: center;\">3.30<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%; text-align: center;\">10\u5206\u5f8c<\/td>\n<td style=\"width: 50%; text-align: center;\">2.17<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%; text-align: center;\">20\u5206\u5f8c<\/td>\n<td style=\"width: 50%; text-align: center;\">0.944<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%; text-align: center;\">30\u5206\u5f8c<\/td>\n<td style=\"width: 50%; text-align: center;\">0.410<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%; text-align: center;\">40\u5206\u5f8c<\/td>\n<td style=\"width: 50%; text-align: center;\">0.178<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%; text-align: center;\">50\u5206\u5f8c<\/td>\n<td style=\"width: 50%; text-align: center;\">0.0775<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%; text-align: center;\">60\u5206\u5f8c<\/td>\n<td style=\"width: 50%; text-align: center;\">0.0337<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u3053\u306e\u3088\u3046\u306b\u3001<span style=\"color: #0000ff;\">\u6642\u9593\u7d4c\u904e\u3068\u5171\u306b\u78ba\u7387\u5bc6\u5ea6\u306f\u4f4e\u304f\u306a\u3063\u3066\u3044\u304d\u307e\u3059\u3002<\/span>\u6a2a\u8ef8\u3092\\(x\\)\u3001\u305f\u3066\u8ef8\u3092\u78ba\u7387\u5bc6\u5ea6\u3068\u3059\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u30b0\u30e9\u30d5\u3092\u63cf\u304f\u306e\u304c\u6307\u6570\u5206\u5e03\u3067\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/05\/fjr7.jpg\" alt=\"\" width=\"445\" height=\"292\" class=\"aligncenter size-full wp-image-6476\" \/><\/p>\n<p>\u3064\u307e\u308a\u6307\u6570\u5206\u5e03\u3067\u306f\u3001\u6b21\u56de\u306e\u30a4\u30d9\u30f3\u30c8\u304c\u767a\u751f\u3059\u308b\u78ba\u7387\u5bc6\u5ea6\u306f\u6700\u521d\u304c\u9ad8\u304f\u3001\u6642\u9593\u7d4c\u904e\u3068\u5171\u306b\u78ba\u7387\u5bc6\u5ea6\u304c\u4f4e\u304f\u306a\u308b\u3068\u8003\u3048\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u306a\u304a\\(\u03bb\\)\u306b\u3088\u3063\u3066\u30b0\u30e9\u30d5\u306e\u5f62\u306f\u5909\u5316\u3057\u307e\u3059\u3002\u5177\u4f53\u7684\u306b\u306f\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308b\u3068\u7406\u89e3\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/05\/fjr8.jpg\" alt=\"\" width=\"444\" height=\"303\" class=\"aligncenter size-full wp-image-6477\" \/><\/p>\n<p>\\(\u03bb\\)\u306f\u6642\u9593\u3054\u3068\u306e\u30a4\u30d9\u30f3\u30c8\u306e\u5e73\u5747\u767a\u751f\u56de\u6570\u3067\u3042\u308a\u30011\u6642\u9593\u3092\u57fa\u6e96\u306b\u3059\u308b\u306e\u304b\u3001\u305d\u308c\u3068\u30821\u5e74\u3092\u57fa\u6e96\u306b\u3059\u308b\u306e\u304b\u306b\u3088\u3063\u3066\\(\u03bb\\)\u306e\u5024\u306f\u7570\u306a\u308a\u307e\u3059\u3002\u3044\u305a\u308c\u306b\u3057\u3066\u3082\u3001\u3053\u306e\u3088\u3046\u306a\u30b0\u30e9\u30d5\u306e\u9055\u3044\u304c\u8868\u308c\u307e\u3059\u3002<\/p>\n<h3>\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\u3092\u5229\u7528\u3057\u3001\u78ba\u7387\u3092\u8a08\u7b97\u3059\u308b<\/h3>\n<p>\u5148\u307b\u3069\u793a\u3057\u305f\u56f3\u306f\u300c\u7279\u5b9a\u306e\u70b9\u3067\u306e\u78ba\u7387\u5bc6\u5ea6\u300d\u3067\u3059\u3002\u305f\u3060\u3001\u7279\u5b9a\u306e\u70b9\u3067\u306e\u78ba\u7387\u3092\u77e5\u3063\u3066\u3082\u5229\u7528\u3059\u308b\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\u3002\u6307\u6570\u5206\u5e03\u3067\u306f\u3001\u305d\u308c\u307e\u3067\u306e\u78ba\u7387\u5206\u5e03\u3092\u3059\u3079\u3066\u8db3\u3059\u3053\u3068\u306b\u3088\u3063\u3066\u3001\u78ba\u7387\u304c\u3082\u3064\u610f\u5473\u3092\u3088\u3046\u3084\u304f\u7406\u89e3\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u5f53\u7136\u306a\u304c\u3089\u3001<span style=\"color: #0000ff;\">\u6642\u9593\u7d4c\u904e\u3068\u5171\u306b\u30a4\u30d9\u30f3\u30c8\u306e\u767a\u751f\u78ba\u7387\u306f\u9ad8\u304f\u306a\u308a\u307e\u3059\u3002<\/span>\u4f8b\u3048\u3070\u4e00\u5b9a\u9593\u9694\u3067\u4ea4\u901a\u4e8b\u6545\u304c\u8d77\u304d\u308b\u306b\u3082\u95a2\u308f\u3089\u305a\u3001\u9577\u304f\u4ea4\u901a\u4e8b\u6545\u304c\u8d77\u304d\u3066\u3044\u306a\u3044\u5834\u5408\u3001\u4ea4\u901a\u4e8b\u6545\u304c\u767a\u751f\u3059\u308b\u78ba\u7387\u306f\u9ad8\u304f\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u305d\u3053\u3067\u7279\u5b9a\u306e\u30dd\u30a4\u30f3\u30c8\u306e\u78ba\u7387\u5bc6\u5ea6\u3067\u306f\u306a\u304f\u3001\u300c\u7279\u5b9a\u306e\u30dd\u30a4\u30f3\u30c8\u306b\u3064\u3044\u3066\u3001\u305d\u308c\u307e\u3067\u306e\u78ba\u7387\u5bc6\u5ea6\u3092\u3059\u3079\u3066\u7d2f\u7a4d\u3057\u305f\u5024\u300d\u3092\u8a08\u7b97\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u7279\u5b9a\u306e\u30dd\u30a4\u30f3\u30c8\u306b\u3064\u3044\u3066\u3001\u3059\u3079\u3066\u306e\u767a\u751f\u78ba\u7387\u3092\u8db3\u3059\u3053\u3068\u306b\u3088\u3063\u3066\u5f97\u3089\u308c\u308b\u95a2\u6570\u3092\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\\(F(x)\\)\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n<p>\u30e9\u30f3\u30c0\u30e0\u3067\u767a\u751f\u3059\u308b\u30a4\u30d9\u30f3\u30c8\u306b\u3064\u3044\u3066\u3001\u6642\u9593\u7d4c\u904e\u304c\u9577\u304f\u306a\u308b\u3068\u518d\u3073\u767a\u751f\u3059\u308b\u78ba\u7387\u304c\u9ad8\u304f\u306a\u308b\u306e\u306f\u3001\u79c1\u305f\u3061\u306e\u611f\u899a\u306b\u3082\u5408\u81f4\u3057\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u3059\u3079\u3066\u306e\u78ba\u7387\u3092\u8db3\u3059\u3053\u3068\u3067\u53ef\u80fd\u306b\u306a\u308b\u306e\u3067\u3059\u3002<\/p>\n<p>\u9023\u7d9a\u578b\u78ba\u7387\u5206\u5e03\u306f\u66f2\u7dda\u306e\u30b0\u30e9\u30d5\u3067\u3059\u3002\u3053\u306e\u5834\u5408\u3001\u7a4d\u5206\u3092\u7528\u3044\u3066\u9762\u7a4d\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<span style=\"color: #ff0000;\">\u9762\u7a4d\u3092\u5f97\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u3001\u3059\u3079\u3066\u306e\u78ba\u7387\u5bc6\u5ea6\u3092\u8db3\u3059\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002<\/span>\u3064\u307e\u308a\u3001\u9762\u7a4d\u304c\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\u306b\u306a\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\/kgje9-1.jpg\" alt=\"\" width=\"446\" height=\"275\" class=\"aligncenter size-full wp-image-6537\" \/><\/p>\n<p>\\(F(a)=\\displaystyle \\int_{0}^{a} \u03bbe^{-\u03bbx} dx\\)<\/p>\n<p>\\(=1-e^{-\u03bba}\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\u306f\\(F(x)=1-e^{-\u03bbx}\\)\u3068\u308f\u304b\u308a\u307e\u3057\u305f\u3002\u3053\u308c\u3092\u30b0\u30e9\u30d5\u306b\u3059\u308b\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\/fjr10.jpg\" alt=\"\" width=\"411\" height=\"272\" class=\"aligncenter size-full wp-image-6479\" \/><\/p>\n<p>\u6307\u6570\u5206\u5e03\u3092\u5229\u7528\u3057\u3066\u6b21\u306e\u30a4\u30d9\u30f3\u30c8\u304c\u767a\u751f\u3059\u308b\u78ba\u7387\u3092\u77e5\u308a\u305f\u3044\u5834\u5408\u3001\u7279\u5b9a\u306e\u30dd\u30a4\u30f3\u30c8\u3067\u306e\u767a\u751f\u78ba\u7387\u3088\u308a\u3082\u3001\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\u3092\u5229\u7528\u3059\u308b\u307b\u3046\u304c\u79c1\u305f\u3061\u306b\u3068\u3063\u3066\u7406\u89e3\u3057\u3084\u3059\u3044\u3067\u3059\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u5148\u307b\u3069\u306e\u4f8b\u984c\u306b\u3064\u3044\u3066\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\u3092\u5229\u7528\u3057\u3066\u554f\u984c\u3092\u89e3\u3044\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>1\u6642\u9593\u306b\u5e73\u57475\u4eba\u304c\u6765\u5e97\u3059\u308b\u5e97\u8217\u304c\u3042\u308a\u307e\u3059\u300210\u5206\u5f8c\u307e\u3067\u306b\u5ba2\u304c\u6765\u5e97\u3059\u308b\u78ba\u7387\u306f\u3044\u304f\u3089\u3067\u3057\u3087\u3046\u304b\u3002<\/li>\n<\/ul>\n<p>10\u5206\u5f8c\u30d4\u30c3\u30bf\u30ea\u306b\u5ba2\u304c\u6765\u5e97\u3059\u308b\u78ba\u7387\u5bc6\u5ea6\u3067\u306f\u306a\u304f\u300110\u5206\u304c\u7d4c\u904e\u3059\u308b\u307e\u3067\u306b\u5ba2\u304c\u6765\u5e97\u3059\u308b\u78ba\u7387\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u3001\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\u3092\u5229\u7528\u3057\u307e\u3057\u3087\u3046\u3002\\(\u03bb=5\\)\u3067\u3042\u308a\u3001\\(x=\\displaystyle\\frac{1}{6}\\)\u306a\u306e\u3067\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\\(1-e^{-\\frac{5}{6}}\u22520.565\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u78ba\u7387\u5bc6\u5ea6\u306e\u5408\u8a08\uff08\u9762\u7a4d\uff09\u306f0.565\uff0856.5%\uff09\u3068\u308f\u304b\u308a\u307e\u3059\u3002\u3053\u3046\u3057\u3066\u3001\u5ba2\u304c\u6765\u5e97\u3059\u308b\u78ba\u7387\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n<h3>\u671f\u5f85\u5024\uff08\u5e73\u5747\uff09\u306e\u8a08\u7b97\u3068\u516c\u5f0f<\/h3>\n<p>\u305d\u308c\u3067\u306f\u3001\u6307\u6570\u5206\u5e03\u306e\u671f\u5f85\u5024\uff08\u5e73\u5747\uff09\u306f\u3069\u306e\u3088\u3046\u306b\u8a08\u7b97\u3059\u308c\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u6307\u6570\u5206\u5e03\u3092\u5229\u7528\u3059\u308b\u3068\u304d\u3001\u4ee5\u4e0b\u306e\u516c\u5f0f\u306b\u3088\u3063\u3066\u671f\u5f85\u5024\\(E(X)\\)\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(E(X)=\\displaystyle\\frac{1}{\u03bb}\\)<\/li>\n<\/ul>\n<p>\u305f\u3060\u3001\u3053\u306e\u516c\u5f0f\u306f\u611f\u899a\u7684\u306b\u7406\u89e3\u3067\u304d\u307e\u3059\u3002\u4f8b\u3048\u30701\u6642\u9593\u306b\u5e73\u57475\u4eba\u304c\u6765\u5e97\u3059\u308b\u5834\u5408\u3001\u5e73\u5747\u3057\u3066\\(\\displaystyle\\frac{1}{5}\\)\u6642\u9593\u3054\u3068\u306b\u5ba2\u304c\u6765\u308b\u3068\u63a8\u6e2c\u3067\u304d\u307e\u3059\u3002\u5358\u4f4d\u6642\u9593\u3042\u305f\u308a\u306b\\(\u03bb\\)\u56de\u306e\u30a4\u30d9\u30f3\u30c8\u304c\u767a\u751f\u3059\u308b\u5834\u5408\u3001\u671f\u5f85\u5024\u304c\\(\\displaystyle\\frac{1}{\u03bb}\\)\u306b\u306a\u308b\u306e\u306f\u5f53\u7136\u3067\u3059\u3002<\/p>\n<p>\u306a\u304a\u671f\u5f85\u5024\u306e\u5b9a\u7fa9\u3092\u5229\u7528\u3059\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a3c\u660e\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\\(E(X)=\\displaystyle \\int_{0}^{\\infty} xf(x) dx\\)<\/p>\n<p>\\(=\u03bb\\displaystyle \\int_{0}^{\\infty} xe^{-\u03bbx} dx\\)<\/p>\n<p>\\(=\\left[-xe^{-\u03bbx}\\right]_0^{\\infty}+\\displaystyle \\int_{0}^{\\infty} e^{-\u03bbx} dx\\)<\/p>\n<p>\\(=0+\\left[-\\displaystyle\\frac{1}{\u03bb}e^{-\u03bbx}\\right]_0^{\\infty}\\)<\/p>\n<p>\\(=\\displaystyle\\frac{1}{\u03bb}\\)<\/p>\n<p>\u9ad8\u6821\u6570\u5b66\u306e\u77e5\u8b58\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u671f\u5f85\u5024\\(E(X)\\)\u304c\\(\\displaystyle\\frac{1}{\u03bb}\\)\u3068\u8a3c\u660e\u3067\u304d\u307e\u3057\u305f\u3002\u305f\u3060\u3053\u3046\u3057\u305f\u8a3c\u660e\u3092\u3057\u306a\u304f\u3066\u3082\u3001\u611f\u899a\u7684\u306b\u6307\u6570\u5206\u5e03\u306e\u671f\u5f85\u5024\uff08\u5e73\u5747\uff09\u306f\\(\\displaystyle\\frac{1}{\u03bb}\\)\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<h3>\u6307\u6570\u5206\u5e03\u3067\u5206\u6563\u306e\u8a08\u7b97\u3092\u884c\u3046<\/h3>\n<p>\u306a\u304a\u671f\u5f85\u5024\u306e\u8a08\u7b97\u3092\u3057\u305f\u5f8c\u3001\u6b21\u306b\u5206\u6563\u306e\u8a08\u7b97\u3092\u884c\u3048\u308b\u3088\u3046\u306b\u3057\u307e\u3057\u3087\u3046\u3002\u6307\u6570\u5206\u5e03\u306e\u5834\u5408\u3001\u671f\u5f85\u5024\u3068\u540c\u3058\u3088\u3046\u306b\u5206\u6563\u306e\u516c\u5f0f\u3082\u5358\u7d14\u3067\u3059\u3002\u4ee5\u4e0b\u304c\u6307\u6570\u5206\u5e03\u3067\u5206\u6563\\(V(X)\\)\u3092\u5f97\u308b\u516c\u5f0f\u3067\u3059\u3002<\/p>\n<ul>\n<li>\\(V(X)=\\displaystyle\\frac{1}{\u03bb^2}\\)<\/li>\n<\/ul>\n<p>\u5206\u6563\u306e\u8a3c\u660e\u306b\u3064\u3044\u3066\u306f\u3001\u5206\u6563\u306e\u5b9a\u7fa9\u3092\u5229\u7528\u3057\u307e\u3057\u3087\u3046\u3002\u3064\u307e\u308a\u3001\u4ee5\u4e0b\u306e\u516c\u5f0f\u3092\u5229\u7528\u3057\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(V(X)=E(X^2)-E(X)^2\\)<\/li>\n<\/ul>\n<p>\\(E(X)=\\displaystyle\\frac{1}{\u03bb}\\)\u3067\u3042\u308b\u305f\u3081\u3001\\(E(X)^2=\\displaystyle\\frac{1}{\u03bb^2}\\)\u3067\u3059\u3002\u305d\u3053\u3067\u3001\\(E(X^2)\\)\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(E(X^2)=\u03bb\\displaystyle \\int_{0}^{\\infty} x^2e^{-\u03bbx} dx\\)<\/p>\n<p>\\(=\\left[-x^2e^{-\u03bbx}\\right]_0^\u221e+\\displaystyle \\int_{0}^{\\infty} 2xe^{-\u03bbx} dx\\)<\/p>\n<p>\u203b\\(\u03bb\\displaystyle \\int_{0}^{\\infty} xe^{-\u03bbx} dx=\\displaystyle\\frac{1}{\u03bb}\\)\u3088\u308a<\/p>\n<p>\\(=0+\\displaystyle\\frac{2}{\u03bb^2}\\)<\/p>\n<p>\\(=\\displaystyle\\frac{2}{\u03bb^2}\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5206\u6563\\(V(X)\\)\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\\(V(X)=E(X^2)-E(X)^2\\)<\/p>\n<p>\\(=\\displaystyle\\frac{2}{\u03bb^2}-\\displaystyle\\frac{1}{\u03bb^2}\\)<\/p>\n<p>\\(=\\displaystyle\\frac{1}{\u03bb^2}\\)<\/p>\n<h2>\u6307\u6570\u5206\u5e03\u306b\u306f\u7121\u8a18\u61b6\u6027\u304c\u3042\u308b<\/h2>\n<p>\u306a\u304a\u6307\u6570\u5206\u5e03\u306b\u306f\u7121\u8a18\u61b6\u6027\u304c\u3042\u308a\u307e\u3059\u3002\u96e2\u6563\u578b\u78ba\u7387\u5206\u5e03\u306e\u5834\u5408\u3001\u5e7e\u4f55\u5206\u5e03\u306e\u307f\u7121\u8a18\u61b6\u6027\u304c\u3042\u308a\u307e\u3059\u3002\u4e00\u65b9\u3067\u9023\u7d9a\u578b\u78ba\u7387\u5206\u5e03\u306e\u5834\u5408\u3001\u7121\u8a18\u61b6\u6027\u3092\u6709\u3059\u308b\u306e\u306f\u6307\u6570\u5206\u5e03\u3060\u3051\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p><span style=\"color: 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