{"id":760,"date":"2023-07-28T20:30:47","date_gmt":"2023-07-28T20:30:47","guid":{"rendered":"https:\/\/statorials.org\/ja\/%e5%b9%be%e4%bd%95%e5%88%86%e5%b8%83\/"},"modified":"2023-07-28T20:30:47","modified_gmt":"2023-07-28T20:30:47","slug":"%e5%b9%be%e4%bd%95%e5%88%86%e5%b8%83","status":"publish","type":"post","link":"https:\/\/statorials.org\/ja\/%e5%b9%be%e4%bd%95%e5%88%86%e5%b8%83\/","title":{"rendered":"\u5e7e\u4f55\u5206\u5e03\u306e\u6982\u8981"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>\u5e7e\u4f55\u5206\u5e03\u306f\u3001<\/strong>\u4e00\u9023\u306e\u30d9\u30eb\u30cc\u30fc\u30a4\u8a66\u884c\u3067\u6700\u521d\u306e\u6210\u529f\u3092\u7d4c\u9a13\u3059\u308b\u524d\u306b\u3001\u4e00\u5b9a\u56de\u6570\u306e\u5931\u6557\u3092\u7d4c\u9a13\u3059\u308b\u78ba\u7387\u3092\u8868\u3057\u307e\u3059\u3002<\/span><\/p>\n<blockquote>\n<p><span style=\"color: #000000;\"><strong>\u30d9\u30eb\u30cc\u30fc\u30a4\u8a66\u884c\u306f<\/strong>\u3001\u300c\u6210\u529f\u300d\u307e\u305f\u306f\u300c\u5931\u6557\u300d\u306e 2 \u3064\u306e\u7d50\u679c\u3057\u304b\u8003\u3048\u3089\u308c\u306a\u3044\u5b9f\u9a13\u3067\u3042\u308a\u3001\u5b9f\u9a13\u304c\u5b9f\u884c\u3055\u308c\u308b\u305f\u3073\u306b\u6210\u529f\u306e\u78ba\u7387\u306f\u540c\u3058\u3067\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u30d9\u30eb\u30cc\u30fc\u30a4\u306e\u30a8\u30c3\u30bb\u30a4\u306e\u4f8b\u3068\u3057\u3066\u306f\u3001\u30b3\u30a4\u30f3\u30c8\u30b9\u304c\u3042\u308a\u307e\u3059\u3002\u30b3\u30a4\u30f3\u306f 2 \u3064\u306e\u8868\u306b\u306e\u307f\u7740\u5730\u3067\u304d\u307e\u3059 (\u8868\u3092\u300c\u30d2\u30c3\u30c8\u300d\u3001\u88cf\u3092\u300c\u5931\u6557\u300d\u3068\u547c\u3073\u307e\u3059)\u3002\u30b3\u30a4\u30f3\u304c\u516c\u6b63\u3067\u3042\u308b\u3068\u4eee\u5b9a\u3059\u308b\u3068\u3001\u5404\u30d5\u30ea\u30c3\u30d7\u3067\u306e\u6210\u529f\u78ba\u7387\u306f 0.5 \u3067\u3059\u3002<\/span><\/p>\n<\/blockquote>\n<p> <span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/ja\/\u30e9\u30f3\u30bf\u3099\u30e0\u5909\u6570\/\" target=\"_blank\" rel=\"noopener\">\u78ba\u7387\u5909\u6570<\/a><em>X \u304c<\/em>\u5e7e\u4f55\u5206\u5e03\u306b\u5f93\u3046\u5834\u5408\u3001\u6700\u521d\u306e\u6210\u529f\u3092\u7d4c\u9a13\u3059\u308b\u524d\u306b<em>k<\/em>\u56de\u306e\u5931\u6557\u3092\u7d4c\u9a13\u3059\u308b\u78ba\u7387\u306f\u3001\u6b21\u306e\u5f0f\u3067\u6c42\u3081\u3089\u308c\u307e\u3059\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X=k) = (1-p) <sup>kp<\/sup><\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u91d1\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>k:<\/strong>\u6700\u521d\u306e\u6210\u529f\u307e\u3067\u306e\u5931\u6557\u56de\u6570<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>p:<\/strong>\u5404\u8a66\u884c\u306e\u6210\u529f\u78ba\u7387<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u305f\u3068\u3048\u3070\u3001\u8868\u304c\u51fa\u308b\u307e\u3067\u516c\u6b63\u306a\u30b3\u30a4\u30f3\u3092\u4f55\u56de\u6295\u3052\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\u304b\u3092\u77e5\u308a\u305f\u3044\u3068\u3057\u307e\u3059\u3002\u4e0a\u8a18\u306e\u5f0f\u3092\u4f7f\u7528\u3057\u3066\u30010\u30011\u30012\u30013 \u56de\u306a\u3069\u306e\u5931\u6557\u304c\u767a\u751f\u3059\u308b\u78ba\u7387\u3092\u6c7a\u5b9a\u3067\u304d\u307e\u3059\u3002\u30b3\u30a4\u30f3\u304c\u8868\u306b\u306a\u308b\u524d\u306b:<\/span><\/p>\n<p><span style=\"color: #000000;\"><em><strong>\u6ce8:<\/strong>\u6700\u521d\u306e\u30c8\u30b9\u3067\u30b3\u30a4\u30f3\u304c\u8868\u306b\u306a\u3063\u305f\u5834\u5408\u3001\u30b3\u30a4\u30f3\u306e\u300c\u5931\u6557\u300d\u306f 0 \u306b\u306a\u308a\u307e\u3059\u3002<\/em><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X=0)<\/strong> = (1-.5) <sup>0<\/sup> (.5) = <strong>0.5<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X=1)<\/strong> = (1-.5) <sup>1<\/sup> (.5) = <strong>0.25<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X=2)<\/strong> = (1-.5) <sup>2<\/sup> (.5) = <strong>0.125<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X=3)<\/strong> = (1-0.5) <sup>3<\/sup> (0.5) = <strong>0.0625<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u30b3\u30a4\u30f3\u6295\u3052\u306e\u78ba\u7387\u3092\u7121\u9650\u5927\u307e\u3067\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002\u6b21\u306b\u3001\u3053\u306e\u78ba\u7387\u5206\u5e03\u3092\u8996\u899a\u5316\u3059\u308b\u305f\u3081\u306e\u5358\u7d14\u306a\u30d2\u30b9\u30c8\u30b0\u30e9\u30e0\u3092\u4f5c\u6210\u3057\u307e\u3059\u3002<\/span> <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-8160 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/geomdist1.png\" alt=\"\u5e7e\u4f55\u78ba\u7387\u5206\u5e03\u30d2\u30b9\u30c8\u30b0\u30e9\u30e0\" width=\"442\" height=\"313\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h3><strong>\u7d2f\u7a4d\u5e7e\u4f55\u78ba\u7387\u306e\u8a08\u7b97<\/strong><\/h3>\n<p>\u6700\u521d\u306e\u6210\u529f\u307e\u3067\u306b k \u4ee5\u4e0b\u306e\u5931\u6557\u3092\u7d4c\u9a13\u3059\u308b\u7d2f\u7a4d\u78ba\u7387\u306f<span style=\"color: #000000;\">\u3001\u6b21\u306e\u5f0f\u3067<\/span><span style=\"color: #000000;\"><em>\u6c42\u3081<\/em><strong>\u3089\u308c<\/strong>\u307e\u3059<\/span>\u3002<\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X\u2264k) = 1 \u2013 (1-p) <sup>k+1<\/sup><\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u91d1\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>k:<\/strong>\u6700\u521d\u306e\u6210\u529f\u307e\u3067\u306e\u5931\u6557\u56de\u6570<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>p:<\/strong>\u5404\u8a66\u884c\u306e\u6210\u529f\u78ba\u7387<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u305f\u3068\u3048\u3070\u3001\u30b3\u30a4\u30f3\u304c\u6700\u7d42\u7684\u306b\u8868\u306b\u306a\u308b\u307e\u3067\u306b 3 \u56de\u4ee5\u4e0b\u306e\u300c\u30df\u30b9\u300d\u304c\u767a\u751f\u3059\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<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X\u22643)<\/strong> = 1 \u2013 (1-0.5) <sup>3+1<\/sup> = <strong>0.9375<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u540c\u69d8\u306e\u5f0f\u3092\u4f7f\u7528\u3057\u3066\u3001\u5404\u7d2f\u7a4d\u78ba\u7387\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X\u22640)<\/strong> = 1 \u2013 (1-.5) <sup>0+1<\/sup> = <strong>0.5<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X\u22641)<\/strong> = 1 \u2013 (1-0.5) <sup>1+1<\/sup> = <strong>0.75<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X\u22642)<\/strong> = 1 \u2013 (1-0.5) <sup>2+1<\/sup> = <strong>0.875<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u3053\u308c\u3089\u306e\u7d2f\u7a4d\u78ba\u7387\u306f\u3001\u30b3\u30a4\u30f3\u3092\u6295\u3052\u308b\u56de\u6570\u3092\u7121\u9650\u306b\u5897\u3084\u3057\u3066\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002\u6b21\u306b\u3001\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<\/span> <\/p>\n<div class=\"wp-block-image\"><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-8162 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/geomdist2.png\" alt=\"\u5e7e\u4f55\u7d2f\u7a4d\u78ba\u7387\u5206\u5e03\" width=\"459\" height=\"283\" srcset=\"\" sizes=\"auto, \"><\/div>\n<h3><strong>\u5e7e\u4f55\u5206\u5e03\u306e\u6027\u8cea<\/strong><\/h3>\n<p><span style=\"color: #000000;\">\u5e7e\u4f55\u5206\u5e03\u306b\u306f\u6b21\u306e\u7279\u6027\u304c\u3042\u308a\u307e\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u5206\u5e03\u306e\u5e73\u5747\u306f<strong>(1-p) \/ p<\/strong>\u3067\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u5206\u5e03\u306e\u5206\u6563\u306f<strong>(1-p) \/ p <sup>2<\/sup><\/strong>\u3067\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4f8b\u3048\u3070\uff1a<\/span><\/p>\n<p><span style=\"color: #000000;\">\u30b3\u30a4\u30f3\u304c\u88cf\u306b\u306a\u308b\u307e\u3067\u306b\u8868\u304c\u51fa\u308b\u5e73\u5747\u56de\u6570\u306f\u3001 (1-p) \/ p = (1-.5) \/ .5 = <strong>1<\/strong>\u3068\u306a\u308a\u307e\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u8868\u306b\u7740\u5730\u3059\u308b\u307e\u3067\u306e\u30c8\u30b9\u6570\u306e\u5206\u6563\u306f\u3001(1-p)\/ <sup>p2<\/sup> =(1-.5)\/ \u3068\u306a\u308a\u307e\u3059\u3002 <sup>52<\/sup> = <strong>2<\/strong> \u3002<\/span><\/p>\n<h3><strong>\u5e7e\u4f55\u5206\u5e03\u306e\u7df4\u7fd2\u554f\u984c<\/strong><\/h3>\n<p><span style=\"color: #000000;\">\u6b21\u306e\u7df4\u7fd2\u554f\u984c\u3092\u4f7f\u7528\u3057\u3066\u3001\u5e7e\u4f55\u5206\u5e03\u306e\u77e5\u8b58\u3092\u30c6\u30b9\u30c8\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\"><em><strong>\u6ce8:<\/strong>\u3053\u308c\u3089\u306e\u8cea\u554f\u306b\u5bfe\u3059\u308b\u7b54\u3048\u3092\u8a08\u7b97\u3059\u308b\u306b\u306f<a href=\"https:\/\/statorials.org\/ja\/\u5e7e\u4f55\u5206\u5e03\u8a08\u7b97\u6a5f\/\" target=\"_blank\" rel=\"noopener\">\u3001\u5e7e\u4f55\u5206\u5e03\u8a08\u7b97\u30c4\u30fc\u30eb<\/a>\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002<\/em><\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u554f\u984c 1<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u8cea\u554f:<\/strong>\u7814\u7a76\u8005\u306f\u56f3\u66f8\u9928\u306e\u5916\u3067\u5f85\u6a5f\u3057\u3001\u7279\u5b9a\u306e\u6cd5\u5f8b\u3092\u652f\u6301\u3059\u308b\u304b\u3069\u3046\u304b\u3092\u4eba\u3005\u306b\u5c0b\u306d\u307e\u3059\u3002\u7279\u5b9a\u306e\u4eba\u304c\u6cd5\u5247\u3092\u652f\u6301\u3059\u308b\u78ba\u7387\u306f p = 0.2 \u3067\u3059\u3002\u7814\u7a76\u8005\u304c\u8a71\u3057\u304b\u3051\u305f 4 \u4eba\u76ee\u306e\u4eba\u304c\u305d\u306e\u6cd5\u5f8b\u3092\u6700\u521d\u306b\u652f\u6301\u3059\u308b\u78ba\u7387\u306f\u3069\u308c\u304f\u3089\u3044\u3067\u3059\u304b?<\/span><\/p>\n<p data-slot-rendered-dynamic=\"true\"><span style=\"color: #000000;\"><strong>\u7b54\u3048:<\/strong>\u6700\u521d\u306e\u6210\u529f\u307e\u3067\u306e\u300c\u5931\u6557\u300d\u306e\u6570\u3001\u3064\u307e\u308a\u3001\u6700\u521d\u306e\u4eba\u304c\u6cd5\u5247\u3092\u652f\u6301\u3059\u308b\u307e\u3067\u305d\u306e\u6cd5\u5247\u3092\u652f\u6301\u3057\u306a\u3044\u4eba\u306e\u6570\u306f 3 \u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001p = 0.2 \u304a\u3088\u3073 x \u3067\u5e7e\u4f55\u5206\u5e03\u8a08\u7b97\u3092\u4f7f\u7528\u3059\u308b\u3068\u3001 = 3 \u56de\u306e\u5931\u6557\u306e\u5834\u5408\u3001 P(X=3) = <strong>0.10240<\/strong>\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u554f\u984c 2<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u8cea\u554f:<\/strong>\u7814\u7a76\u8005\u306f\u56f3\u66f8\u9928\u306e\u5916\u3067\u5f85\u6a5f\u3057\u3001\u7279\u5b9a\u306e\u6cd5\u5f8b\u3092\u652f\u6301\u3059\u308b\u304b\u3069\u3046\u304b\u3092\u4eba\u3005\u306b\u5c0b\u306d\u307e\u3059\u3002\u7279\u5b9a\u306e\u4eba\u304c\u6cd5\u5247\u3092\u652f\u6301\u3059\u308b\u78ba\u7387\u306f p = 0.2 \u3067\u3059\u3002\u7814\u7a76\u8005\u304c\u3053\u306e\u6cd5\u5f8b\u3092\u652f\u6301\u3059\u308b\u4eba\u3092\u898b\u3064\u3051\u308b\u305f\u3081\u306b 4 \u4eba<em>\u4ee5\u4e0a\u306e<\/em>\u4eba\u3068\u8a71\u3092\u3057\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\u78ba\u7387\u306f\u3069\u308c\u304f\u3089\u3044\u3067\u3059\u304b?<\/span><\/p>\n<p data-slot-rendered-dynamic=\"true\"><span style=\"color: #000000;\"><strong>\u56de\u7b54:<\/strong> p =0.2 \u304a\u3088\u3073 x = 4 \u56de\u306e\u5931\u6557\u3067\u5e7e\u4f55\u5206\u5e03\u8a08\u7b97\u3092\u4f7f\u7528\u3059\u308b\u3068\u3001 P(X&gt;4) = <strong>0.32768<\/strong>\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u554f\u984c 3<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u8cea\u554f:<\/strong>\u7814\u7a76\u8005\u306f\u56f3\u66f8\u9928\u306e\u5916\u3067\u5f85\u6a5f\u3057\u3001\u7279\u5b9a\u306e\u6cd5\u5f8b\u3092\u652f\u6301\u3059\u308b\u304b\u3069\u3046\u304b\u3092\u4eba\u3005\u306b\u5c0b\u306d\u307e\u3059\u3002\u7279\u5b9a\u306e\u4eba\u304c\u6cd5\u5247\u3092\u652f\u6301\u3059\u308b\u78ba\u7387\u306f p = 0.2 \u3067\u3059\u3002\u3053\u306e\u6cd5\u5f8b\u3092\u652f\u6301\u3059\u308b\u4eba\u3092\u898b\u3064\u3051\u308b\u307e\u3067\u3001\u7814\u7a76\u8005\u306f\u4f55\u4eba\u306e\u4eba\u3068\u8a71\u3059\u5fc5\u8981\u304c\u3042\u308b\u3068\u4e88\u60f3\u3055\u308c\u307e\u3059\u304b?<\/span><\/p>\n<p data-slot-rendered-dynamic=\"true\"><span style=\"color: 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