{"id":765,"date":"2023-07-28T20:06:46","date_gmt":"2023-07-28T20:06:46","guid":{"rendered":"https:\/\/statorials.org\/ja\/%e8%b2%a0%e3%81%ae%e4%ba%8c%e9%a0%85%e5%88%86%e5%b8%83\/"},"modified":"2023-07-28T20:06:46","modified_gmt":"2023-07-28T20:06:46","slug":"%e8%b2%a0%e3%81%ae%e4%ba%8c%e9%a0%85%e5%88%86%e5%b8%83","status":"publish","type":"post","link":"https:\/\/statorials.org\/ja\/%e8%b2%a0%e3%81%ae%e4%ba%8c%e9%a0%85%e5%88%86%e5%b8%83\/","title":{"rendered":"\u8ca0\u306e\u4e8c\u9805\u5206\u5e03\u306e\u6982\u8981"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>\u8ca0\u306e\u4e8c\u9805\u5206\u5e03\u306f\u3001<\/strong>\u4e00\u9023\u306e\u30d9\u30eb\u30cc\u30fc\u30a4\u8a66\u884c\u306b\u304a\u3044\u3066\u4e00\u5b9a\u56de\u6570\u306e\u6210\u529f\u3092\u7d4c\u9a13\u3059\u308b\u524d\u306b\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;\"><em>\u78ba\u7387<\/em><a href=\"https:\/\/statorials.org\/ja\/\u30e9\u30f3\u30bf\u3099\u30e0\u5909\u6570\/\" target=\"_blank\" rel=\"noopener\">\u5909\u6570<\/a><em>\u306e<\/em><i>\u5834\u5408<\/i><\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>P(X=k) =<\/strong> <strong><sub>k+r-1<\/sub> C <sub>k<\/sub> * (1-p) <sup>r<\/sup> *p <sup>k<\/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>\u5931\u6557\u56de\u6570<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>r:<\/strong>\u6210\u529f\u56de\u6570<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>p:<\/strong>\u4e0e\u3048\u3089\u308c\u305f\u8a66\u884c\u306e\u6210\u529f\u78ba\u7387<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong><sub>k+r-1<\/sub> C <sub>k<\/sub> :<\/strong>\u4e00\u5ea6\u306b k \u500b\u306e (k+r-1) \u500b\u306e\u3082\u306e\u306e\u7d44\u307f\u5408\u308f\u305b\u306e\u6570<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u305f\u3068\u3048\u3070\u3001\u30b3\u30a4\u30f3\u3092\u6295\u3052\u3066\u3001\u8868\u304c\u7740\u5730\u3057\u305f\u3053\u3068\u3092\u300c\u6210\u529f\u300d\u30a4\u30d9\u30f3\u30c8\u3068\u5b9a\u7fa9\u3059\u308b\u3068\u3057\u307e\u3059\u3002\u5408\u8a08 4 \u56de\u306e\u6210\u529f\u3092\u7d4c\u9a13\u3059\u308b\u524d\u306b 6 \u56de\u306e\u5931\u6557\u3092\u7d4c\u9a13\u3059\u308b\u78ba\u7387\u306f\u3069\u308c\u304f\u3089\u3044\u3067\u3059\u304b?<\/span><\/p>\n<p><span style=\"color: #000000;\">\u3053\u306e\u8cea\u554f\u306b\u7b54\u3048\u308b\u305f\u3081\u306b\u3001\u6b21\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u3092\u4f7f\u7528\u3057\u3066\u8ca0\u306e\u4e8c\u9805\u5206\u5e03\u3092\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>k:<\/strong>\u5931\u6557\u6570 = 6<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>r:<\/strong>\u6210\u529f\u56de\u6570 = 4<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>p:<\/strong>\u7279\u5b9a\u306e\u8a66\u884c\u306e\u6210\u529f\u78ba\u7387 = 0.5<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u3053\u308c\u3089\u306e\u6570\u5024\u3092\u5f0f\u306b\u4ee3\u5165\u3059\u308b\u3068\u3001\u78ba\u7387\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X=6 \u5931\u6557)<\/strong> = <sub>6+4-1<\/sub> C <sub>6<\/sub> * (1-.5) <sup>4<\/sup> *(.5) <sup>6<\/sup> = (84)*(.0625)*(.015625) = <strong>0.08203<\/strong> \u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u8ca0\u306e\u4e8c\u9805\u5206\u5e03\u306e\u7279\u6027<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u8ca0\u306e\u4e8c\u9805\u5206\u5e03\u306b\u306f\u6b21\u306e\u7279\u6027\u304c\u3042\u308a\u307e\u3059\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\"><em>r \u56de\u306e<\/em>\u6210\u529f\u3092\u5f97\u308b\u307e\u3067\u306b\u4e88\u60f3\u3055\u308c\u308b\u5931\u6557\u306e\u5e73\u5747\u6570\u306f\u3001 <strong>pr\/(1-p)<\/strong>\u3067\u3059\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\"><em>r<\/em>\u56de\u306e\u6210\u529f\u3092\u5f97\u308b\u307e\u3067\u306b\u4e88\u60f3\u3055\u308c\u308b\u5931\u6557\u306e\u6570\u306e\u5206\u6563\u306f\u3001 <strong>pr<\/strong> <strong>\/ (1-p) <sup>2<\/sup><\/strong>\u3067\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u305f\u3068\u3048\u3070\u3001\u30b3\u30a4\u30f3\u3092\u6295\u3052\u3066\u3001\u8868\u304c\u7740\u5730\u3057\u305f\u3053\u3068\u3092\u300c\u6210\u529f\u300d\u30a4\u30d9\u30f3\u30c8\u3068\u5b9a\u7fa9\u3059\u308b\u3068\u3057\u307e\u3059\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\">4 \u56de\u6210\u529f\u3059\u308b\u307e\u3067\u306b\u4e88\u60f3\u3055\u308c\u308b\u5e73\u5747\u5931\u6557\u6570 (\u4f8b: \u5c3e\u90e8\u7740\u9678)<strong>\u306f\u3001 pr\/(1-p)<\/strong> = (.5*4) \/ (1-.5) = <strong>4<\/strong>\u3068\u306a\u308a\u307e\u3059\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\">4 \u56de\u6210\u529f\u3059\u308b\u307e\u3067\u306b\u4e88\u60f3\u3055\u308c\u308b\u5931\u6557\u6570\u306e\u5206\u6563\u306f<strong>\u3001 pr\/(1-p) <sup>2<\/sup><\/strong> = (.5*4)\/(1-.5) <sup>2<\/sup> = <strong>8<\/strong>\u3068\u306a\u308a\u307e\u3059\u3002<\/span><\/p>\n<h3><strong>\u8ca0\u306e\u4e8c\u9805\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\u8ca0\u306e\u4e8c\u9805\u5206\u5e03\u306b\u95a2\u3059\u308b\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\/\u8ca0\u306e\u4e8c\u9805\u5206\u5e03\u8a08\u7b97\u6a5f\/\" target=\"_blank\" rel=\"noopener\">\u3001\u8ca0\u306e\u4e8c\u9805\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>\u30b3\u30a4\u30f3\u3092\u6295\u3052\u3066\u3001\u8868\u304c\u51fa\u308b\u5834\u5408\u3092\u300c\u6210\u529f\u300d\u30a4\u30d9\u30f3\u30c8\u3068\u5b9a\u7fa9\u3059\u308b\u3068\u3057\u307e\u3059\u3002\u5408\u8a08 4 \u56de\u306e\u6210\u529f\u3092\u7d4c\u9a13\u3059\u308b\u524d\u306b 3 \u56de\u306e\u5931\u6557\u3092\u7d4c\u9a13\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>\u56de\u7b54:<\/strong> k = 3 \u56de\u306e\u5931\u6557\u3001r = 4 \u56de\u306e\u6210\u529f\u3001\u304a\u3088\u3073 p = 0.5 \u3067\u8ca0\u306e\u4e8c\u9805\u5206\u5e03\u8a08\u7b97\u3092\u4f7f\u7528\u3059\u308b\u3068\u3001 P(X=3) = <strong>0.15625<\/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>\u6238\u5225\u8a2a\u554f\u3057\u3066\u304a\u83d3\u5b50\u3092\u58f2\u308a\u6b69\u3044\u305f\u3068\u3057\u307e\u3059\u3002\u8ab0\u304b\u304c\u30ad\u30e3\u30f3\u30c7\u30a3\u30fc\u30d0\u30fc\u3092\u8cb7\u3063\u3066\u304f\u308c\u305f\u3089\u3001\u79c1\u305f\u3061\u306f\u305d\u308c\u3092\u300c\u6210\u529f\u300d\u3060\u3068\u8003\u3048\u307e\u3059\u3002\u7279\u5b9a\u306e\u4eba\u304c\u30ad\u30e3\u30f3\u30c7\u30a3\u30fc \u30d0\u30fc\u3092\u8cfc\u5165\u3059\u308b\u78ba\u7387\u306f 0.4 \u3067\u3059\u3002\u5408\u8a08 5 \u56de\u306e\u6210\u529f\u3092\u7d4c\u9a13\u3059\u308b\u524d\u306b 8 \u56de\u306e\u5931\u6557\u3092\u7d4c\u9a13\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>\u56de\u7b54:<\/strong> k = 8 \u56de\u306e\u5931\u6557\u3001r = 5 \u56de\u306e\u6210\u529f\u3001\u304a\u3088\u3073 p = 0.4 \u3067\u8ca0\u306e\u4e8c\u9805\u5206\u5e03\u8a08\u7b97\u30c4\u30fc\u30eb\u3092\u4f7f\u7528\u3059\u308b\u3068\u3001 P(X=8) = <strong>0.08514<\/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>\u30b5\u30a4\u30b3\u30ed\u3092\u632f\u3063\u3066\u3001\u6570\u5b57\u306e 5 \u304c\u51fa\u308b\u3053\u3068\u3092\u300c\u6210\u529f\u300d\u3068\u5b9a\u7fa9\u3059\u308b\u3068\u3057\u307e\u3059\u3002\u4e0e\u3048\u3089\u308c\u305f\u51fa\u76ee\u3067\u30b5\u30a4\u30b3\u30ed\u304c 5 \u306b\u306a\u308b\u78ba\u7387\u306f\u30011\/6 = 0.167 \u3067\u3059\u3002\u5408\u8a08 3 \u56de\u306e\u6210\u529f\u3092\u7d4c\u9a13\u3059\u308b\u524d\u306b 4 \u56de\u306e\u5931\u6557\u3092\u7d4c\u9a13\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>\u56de\u7b54:<\/strong> k = 4 \u56de\u306e\u5931\u6557\u3001r = 3 \u56de\u306e\u6210\u529f\u3001\u304a\u3088\u3073 p = 0.167 \u3067\u8ca0\u306e\u4e8c\u9805\u5206\u5e03\u8a08\u7b97\u3092\u4f7f\u7528\u3059\u308b\u3068\u3001 P(X=4) = <strong>0.03364<\/strong>\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u8ca0\u306e\u4e8c\u9805\u5206\u5e03\u306f\u3001\u4e00\u9023\u306e\u30d9\u30eb\u30cc\u30fc\u30a4\u8a66\u884c\u306b\u304a\u3044\u3066\u4e00\u5b9a\u56de\u6570\u306e\u6210\u529f\u3092\u7d4c\u9a13\u3059\u308b\u524d\u306b\u4e00\u5b9a\u56de\u6570\u306e\u5931\u6557\u3092\u7d4c\u9a13\u3059\u308b\u78ba\u7387\u3092\u8868\u3057\u307e\u3059\u3002 \u30d9\u30eb\u30cc\u30fc\u30a4\u8a66\u884c\u306f\u3001\u300c\u6210\u529f\u300d\u307e\u305f\u306f\u300c\u5931\u6557\u300d\u306e 2 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