{"id":2119,"date":"2019-09-12T22:38:04","date_gmt":"2019-09-12T13:38:04","guid":{"rendered":"http:\/\/www.python.ambitious-engineer.com\/?p=2119"},"modified":"2020-10-04T22:34:07","modified_gmt":"2020-10-04T13:34:07","slug":"%e7%a2%ba%e7%8e%87%e5%a4%89%e6%95%b0%e3%81%a8%e5%88%86%e5%b8%83","status":"publish","type":"post","link":"https:\/\/www.python.ambitious-engineer.com\/archives\/2119","title":{"rendered":"\u78ba\u7387\u5909\u6570\u3068\u5206\u5e03"},"content":{"rendered":"<p><script async src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mathjax\/2.7.0\/MathJax.js?config=TeX-AMS_CHTML\"><\/script><\/p>\n<p>\u3053\u308c\u307e\u3067\u3001\u30c7\u30fc\u30bf\u306e\u7279\u5fb4\u3092\u3068\u3089\u3048\u308b\u305f\u3081\u5e73\u5747\u3084\u5206\u6563\u306a\u3069\u306e\u7d71\u8a08\u91cf\u306b\u3064\u3044\u3066\u5b66\u7fd2\u3057\u3066\u304d\u307e\u3057\u305f\u3002\u3053\u3053\u304b\u3089\u306f\u5c11\u3057\u96e3\u3057\u304f\u306a\u308a\u307e\u3059\u304c\u3001\u78ba\u7387\u5909\u6570\u306b\u3064\u3044\u3066\u5b66\u7fd2\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<h2>\u78ba\u7387\u5909\u6570\u3068\u5206\u5e03<\/h2>\n<h3>\u96e2\u6563\u578b\u78ba\u7387\u5909\u6570<\/h3>\n<p>\u30b5\u30a4\u30b3\u30ed\u306e\u76ee\u306e\u3088\u3046\u306b\u5404\u5909\u6570\u306b\u5bfe\u3057\u3066\u78ba\u7387\u304c\u4e0e\u3048\u3089\u308c\u3066\u3044\u308b\u5834\u5408\u3001\u305d\u308c\u3089\u306e\u5404\u5909\u6570\u3092\u78ba\u7387\u5909\u6570\u3068\u547c\u3073\u307e\u3059\u3002\u78ba\u7387\u7684\u306b\u8272\u3005\u306a\u5024\u3092\u53d6\u308a\u3046\u308b\u5909\u6570\u3068\u3082\u3044\u3048\u307e\u3059\u3002\u78ba\u7387\u5909\u6570\u304c\u3068\u308b\u5206\u5e03\u3092\u78ba\u7387\u5206\u5e03\u3068\u547c\u3073\u307e\u3059\u3002<\/p>\n<p>\u307e\u305f\u30016\u9762\u306e\u30b5\u30a4\u30b3\u30ed\u306f\u221a2\u306a\u3069\u306e\u9593\u306f\u5b58\u5728\u305b\u305a\u3001\u98db\u3073\u98db\u3073\u306e\u5024\u3092\u3068\u308a\u307e\u3059\u304c\u3001\u3053\u306e\u3088\u3046\u306a\u78ba\u7387\u5909\u6570\u3092\u96e2\u6563\u578b\u78ba\u7387\u5909\u6570\u3068\u547c\u3073\u307e\u3059\u3002\u4e00\u65b9\u3001\u9023\u7d9a\u7684\u306a\u5024\u3092\u53d6\u308b\u78ba\u7387\u5909\u6570\u3082\u3042\u308a\u9023\u7d9a\u578b\u78ba\u7387\u5909\u6570\u3068\u547c\u3073\u307e\u3059\u304c\u3001\u307e\u305a\u306f\u96e2\u6563\u578b\u78ba\u7387\u5909\u6570\u304b\u3089\u89e3\u8aac\u3057\u307e\u3059\u3002<\/p>\n<p>6\u9762\u306e\u30b5\u30a4\u30b3\u30ed\u3092\u9069\u5f53\u306b\u632f\u308b\u30681\u301c6\u306e\u76ee\u306f\u305d\u308c\u305e\u308c1\/6\u306e\u78ba\u7387\u3067\u51fa\u73fe\u3057\u307e\u3059\u3002\u307e\u305f\u3001\u305d\u308c\u4ee5\u5916\u306e\u76ee\u304c\u51fa\u308b\u78ba\u7387\u306f\u3042\u308a\u3048\u306a\u3044\u306e\u30670\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n<table>\n<tr>\n<th>\u78ba\u7387\u5909\u6570<\/th>\n<td>1<\/td>\n<td>2<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td>6<\/td>\n<\/tr>\n<tr>\n<th>\u78ba\u7387<\/th>\n<td>1\/6<\/td>\n<td>1\/6<\/td>\n<td>1\/6<\/td>\n<td>1\/6<\/td>\n<td>1\/6<\/td>\n<td>1\/6<\/td>\n<\/tr>\n<\/table>\n<p>\u30b5\u30a4\u30b3\u30ed\u306e\u51fa\u308b\u76ee\u306e\u78ba\u7387\u306e\u95a2\u6570\u3092\u3068\u3057\u3066\u8868\u3059\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306a\u96e2\u6563\u578b\u78ba\u7387\u5909\u6570\u306e\u95a2\u6570\u3092\u78ba\u7387\u8cea\u91cf\u95a2\u6570\u3068\u547c\u3073\u307e\u3059\u3002\u82f1\u8a9e\u3067\u306fprobability mass function\u3068\u547c\u3070\u308c\u3001PMF\u3068\u7565\u3055\u308c\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<p>\\[f(X) = \\begin{cases}<br \/>\n    1\/6 & (x\u304c1, 2, 3, 4, 5, 6 \u306e\u3044\u305a\u308c\u304b) \\\\<br \/>\n    0 & (\u4e0a\u8a18\u4ee5\u5916)<br \/>\n  \\end{cases} \\]\n<p>\u30b0\u30e9\u30d5\u306b\u3059\u308b\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002X\u8ef8\u304c\u78ba\u7387\u5909\u6570\u3001\u30b0\u30e9\u30d5\u306e\u9ad8\u3055\u304c\u78ba\u7387\u3067\u3059\u3002<\/p>\n<p><a href=\"http:\/\/www.python.ambitious-engineer.com\/wp-content\/uploads\/2019\/09\/dice_pmf-1.png\"><img loading=\"lazy\" src=\"http:\/\/www.python.ambitious-engineer.com\/wp-content\/uploads\/2019\/09\/dice_pmf-1.png\" alt=\"\" width=\"816\" height=\"562\" class=\"alignnone size-full wp-image-2342\" srcset=\"https:\/\/www.python.ambitious-engineer.com\/wp-content\/uploads\/2019\/09\/dice_pmf-1.png 816w, https:\/\/www.python.ambitious-engineer.com\/wp-content\/uploads\/2019\/09\/dice_pmf-1-300x207.png 300w, https:\/\/www.python.ambitious-engineer.com\/wp-content\/uploads\/2019\/09\/dice_pmf-1-768x529.png 768w\" sizes=\"(max-width: 816px) 100vw, 816px\" \/><\/a><br \/>\n\u30b0\u30e9\u30d5\u3092\u898b\u308b\u3068\u30011\u301c6\u306e\u5404\u5024\u3067\u78ba\u73871\/6\u304c\u3001\u305d\u308c\u4ee5\u5916\u306e\u70b9\u306f\u78ba\u73870\u3068\u306a\u3063\u3066\u3044\u308b\u3053\u3068\u304c\u8868\u3055\u308c\u3066\u3044\u308b\u3068\u3044\u3046\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u4e0a\u306e\u30b0\u30e9\u30d5\u306e\u3068\u304a\u308a\u3001\u96e2\u6563\u578b\u78ba\u7387\u5909\u6570\u306fX\u306e\u3042\u308b\u70b9\u306b\u5bfe\u3057\u3066Y\u306e\u78ba\u7387\u304c\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002<\/p>\n<h3>\u9023\u7d9a\u578b\u78ba\u7387\u5909\u6570<\/h3>\n<p>\u30b5\u30a4\u30b3\u30ed\u3084\u30af\u30b8\u306a\u3069\u3001\u96e2\u6563\u578b\u306e\u78ba\u7387\u306f\u4e2d\u5b66\u30fb\u9ad8\u6821\u306e\u6570\u5b66\u306e\u6388\u696d\u3067\u6271\u3046\u305f\u3081\u6bd4\u8f03\u7684\u99b4\u67d3\u307f\u304c\u3042\u308a\u307e\u3059\u304c\u3001\u7d71\u8a08\u3092\u5b66\u3076\u4e0a\u3067\u3082\u3046\u4e00\u3064\u91cd\u8981\u306a\u306e\u304c\u9023\u7d9a\u578b\u78ba\u7387\u5909\u6570\u3067\u3059\u3002<\/p>\n<p>\u307e\u305a\u3001\u30af\u30a4\u30ba\u304b\u3089\u3084\u3063\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<p><strong>\u30af\u30a4\u30ba<\/strong><br \/>\n\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u56de\u8ee2\u3059\u308b\u30dc\u30fc\u30c9\u306b\u5439\u304d\u77e2\u3092\u5f53\u3066\u3066\u307f\u308b\u3002\u30dc\u30fc\u30c9\u306b\u306f\u89d2\u5ea6\u304c\u632f\u3089\u308c\u3066\u3044\u308b\u3002\u5439\u304d\u77e2\u306f\u30dc\u30fc\u30c9\u306e\u3069\u3053\u304b\u306b\u30e9\u30f3\u30c0\u30e0\u306b\u547d\u4e2d\u3059\u308b\u3082\u306e\u3068\u3059\u308b\u3002\u307e\u305f\u3001\u30dc\u30fc\u30c9\u304b\u3089\u5916\u308c\u308b\u3053\u3068\u306f\u306a\u3044\u3082\u306e\u3068\u3059\u308b\u3002<\/p>\n<a href=\"http:\/\/www.python.ambitious-engineer.com\/wp-content\/uploads\/2019\/09\/fukiya.png\"><img loading=\"lazy\" src=\"http:\/\/www.python.ambitious-engineer.com\/wp-content\/uploads\/2019\/09\/fukiya-1024x565.png\" alt=\"\" width=\"640\" height=\"353\" class=\"alignnone size-large wp-image-2323\" srcset=\"https:\/\/www.python.ambitious-engineer.com\/wp-content\/uploads\/2019\/09\/fukiya-1024x565.png 1024w, https:\/\/www.python.ambitious-engineer.com\/wp-content\/uploads\/2019\/09\/fukiya-300x166.png 300w, https:\/\/www.python.ambitious-engineer.com\/wp-content\/uploads\/2019\/09\/fukiya-768x424.png 768w, https:\/\/www.python.ambitious-engineer.com\/wp-content\/uploads\/2019\/09\/fukiya.png 1102w\" sizes=\"(max-width: 640px) 100vw, 640px\" \/><\/a>\n<p>(1) 0\u5ea6\u301c90\u5ea6\u306e\u9593\u306b\u547d\u4e2d\u3059\u308b\u78ba\u7387\u3092\u6c42\u3081\u3088<br \/>\n(2) 90\u5ea6\u306e\u7dda\u306b\u304d\u3063\u3061\u308a\u547d\u4e2d\u3059\u308b\u78ba\u7387\u3092\u6c42\u3081\u3088<\/p>\n<p>&nbsp;<\/p>\n<p>\u3055\u3066\u3001\u308f\u304b\u3063\u305f\u3067\u3057\u3087\u3046\u304b\uff1f<\/p>\n<p>\u307e\u305a\u3001(1)\u306e\u7b54\u3048\u306f1\/4\u3068\u306a\u308a\u307e\u3059\u3002\u3069\u306e\u70b9\u3067\u3082\u30e9\u30f3\u30c0\u30e0\u306b\u5f53\u305f\u308b\u306e\u3067\u3001\u5168\u4f53\u306e1\/4\u9818\u57df\u3067\u3042\u308b0\u5ea6\u301c90\u5ea6\u306e\u5834\u6240\u306b\u547d\u4e2d\u3059\u308b\u78ba\u7387\u306f1\/4\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>(2)\u306a\u306e\u3067\u3059\u304c\u3001\u7b54\u3048\u306f0\u3068\u306a\u308a\u307e\u3059\u3002\u3053\u3061\u3089\u306f\u60a9\u307e\u308c\u305f\u65b9\u304c\u7d50\u69cb\u3044\u308b\u306e\u3067\u306f\u306a\u3044\u3067\u3057\u3087\u3046\u304b\u3002\u89d2\u5ea6\u306e\u3088\u3046\u306b\u9023\u7d9a\u306a\u5024\u3092\u3068\u308b\u3082\u306e\u306f\u3001\u4efb\u610f\u306e\u4e00\u70b9\u304c\u767a\u751f\u3059\u308b\u78ba\u7387\u306f0\u3068\u306a\u308a\u307e\u3059\u3002\u96d1\u306a\u8aac\u660e\u3092\u3059\u308b\u3068\u3001\u70b9\u306e\u6570\u306f\u221e\u306a\u306e\u3067\u3001\u3042\u308b\u70b9\u306b\u547d\u4e2d\u3059\u308b\u78ba\u7387\u306f1\/\u221e=0\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u89d2\u5ea6\u306e\u3088\u3046\u306a\u9023\u7d9a\u7684\u306a\u5024\u3092\u3068\u308b\u78ba\u7387\u5909\u6570\u3092\u9023\u7d9a\u578b\u78ba\u7387\u5909\u6570\u3068\u547c\u3073\u307e\u3059\u3002\u4e0a\u306e\u5186\u76e4\u306e\u89d2\u5ea6\\(-\\pi\\sim\\pi\\)\uff08\u5358\u4f4d\u306f\u30e9\u30b8\u30a2\u30f3\u3068\u3057\u307e\u3059\u3002\uff09\u3092\u78ba\u7387\u5909\u6570\u3068\u3057\u3066\u307f\u306a\u3057\u305f\u3068\u304d\u306e\u95a2\u6570\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<br \/>\n\\[f(X) = \\begin{cases}<br \/>\n    1\/(2\\pi) & (-\\pi <= x < \\pi) \\\\\n    0 & (\u4e0a\u4ee5\u5916\u306e\u5834\u5408)\n  \\end{cases} \\]\n\n\u3053\u306e\u3088\u3046\u306a\u9023\u7d9a\u578b\u78ba\u7387\u5909\u6570\u306e\u78ba\u7387\u306e\u95a2\u6570\u3092\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u3068\u547c\u3073\u307e\u3059\u3002\u82f1\u8a9e\u3060\u3068probability density function\u3067\u7565\u3057\u3066PDF\u3068\u547c\u3070\u308c\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002\u5148\u7a0b\u306e\u95a2\u6570\u3092\u30b0\u30e9\u30d5\u3067\u8868\u3059\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002\n<a href=\"http:\/\/www.python.ambitious-engineer.com\/wp-content\/uploads\/2019\/09\/darts_pdf.png\"><img loading=\"lazy\" src=\"http:\/\/www.python.ambitious-engineer.com\/wp-content\/uploads\/2019\/09\/darts_pdf.png\" alt=\"\" width=\"798\" height=\"522\" class=\"alignnone size-full wp-image-2327\" srcset=\"https:\/\/www.python.ambitious-engineer.com\/wp-content\/uploads\/2019\/09\/darts_pdf.png 798w, https:\/\/www.python.ambitious-engineer.com\/wp-content\/uploads\/2019\/09\/darts_pdf-300x196.png 300w, https:\/\/www.python.ambitious-engineer.com\/wp-content\/uploads\/2019\/09\/darts_pdf-768x502.png 768w\" sizes=\"(max-width: 798px) 100vw, 798px\" \/><\/a><\/p>\n<p>\u30b0\u30e9\u30d5\u306e\u898b\u65b9\u306a\u306e\u3067\u3059\u304c\u3001\u6307\u5b9a\u7bc4\u56f2\u3067\u306e\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u3068x\u8ef8\u56f2\u307e\u308c\u305f\u90e8\u5206\u306e\u9762\u7a4d\u304c\u305d\u306e\u7bc4\u56f2\u304c\u8d77\u3053\u308a\u3046\u308b\u78ba\u7387\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u4f8b\u3048\u3070\u3001\u5148\u7a0b\u306e0\u5ea6\u301c90\u5ea6\\(0\\sim\\frac{\\pi}{2}\\)\u306e\u9593\u306b\u547d\u4e2d\u3059\u308b\u78ba\u7387\u306e\u5834\u5408\u306e\u78ba\u7387\u3092\u56f3\u793a\u3057\u305f\u5834\u5408\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u3001\u56f2\u307e\u308c\u305f\u90e8\u5206\u306e\u9762\u7a4d\u306f1\/4\u3067\u3059\u3002\u3053\u306e1\/4\u304c\u5439\u304d\u77e2\u304c0\u5ea6\u301c90\u5ea6\u306e\u9593\u306b\u547d\u4e2d\u3059\u308b\u78ba\u7387\u3068\u306a\u308a\u307e\u3059\u3002<br \/>\n<a href=\"http:\/\/www.python.ambitious-engineer.com\/wp-content\/uploads\/2019\/09\/darts_pdf_q.png\"><img loading=\"lazy\" src=\"http:\/\/www.python.ambitious-engineer.com\/wp-content\/uploads\/2019\/09\/darts_pdf_q.png\" alt=\"\" width=\"804\" height=\"544\" class=\"alignnone size-full wp-image-2329\" srcset=\"https:\/\/www.python.ambitious-engineer.com\/wp-content\/uploads\/2019\/09\/darts_pdf_q.png 804w, https:\/\/www.python.ambitious-engineer.com\/wp-content\/uploads\/2019\/09\/darts_pdf_q-300x203.png 300w, https:\/\/www.python.ambitious-engineer.com\/wp-content\/uploads\/2019\/09\/darts_pdf_q-768x520.png 768w\" sizes=\"(max-width: 804px) 100vw, 804px\" \/><\/a><\/p>\n<p>\u307e\u305f\u3001\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u3068x\u8ef8\u3067\u56f2\u307e\u308c\u305f\u90e8\u5206\u306e\u9762\u7a4d\u306f1\u3068\u306a\u308a\u307e\u3059\u304c\u3001\u3053\u308c\u306f\u5168\u4e8b\u8c61\u306e\u78ba\u7387\u3092\u8868\u3057\u307e\u3059\u3002\u4e00\u65b9\u3067\u4efb\u610f\u306e\u70b9\u306e\u767a\u751f\u3059\u308b\u78ba\u7387\u306f0\u3068\u306a\u308a\u307e\u3059\u30021\u3064\u306e\u70b9\u306b\u5bfe\u5fdc\u3059\u308b\u9ad8\u3055\u306b\u306f\u3042\u307e\u308a\u610f\u5473\u304c\u306a\u304f\u3001\u91cd\u8981\u306a\u306e\u306f\u9023\u7d9a\u578b\u78ba\u7387\u5909\u6570\u306f\u70b9\u3067\u306f\u306a\u304f\u7bc4\u56f2\u3067\u6271\u3046\u3001\u3068\u3044\u3046\u3053\u3068\u3067\u3059\u3002<\/p>\n<p>\u3053\u306e\u5186\u76e4\u306e\u89d2\u5ea6\u306e\u4f8b\u306e\u3088\u3046\u306a\u7279\u5b9a\u306e\u7bc4\u56f2\u304c\u4e00\u5b9a\u306e\u5206\u5e03\u3092\u4e00\u69d8\u5206\u5e03\u3068\u547c\u3073\u307e\u3059\u3002\u5c11\u3005\u96e3\u3057\u3044\u5185\u5bb9\u3067\u3057\u305f\u304c\u3053\u3053\u3092\u62bc\u3055\u3048\u308c\u3070\u4eca\u5f8c\u3001\u7279\u5b9a\u306e\u5206\u5e03\u3067\u3042\u308c\u3070Python\u3067\u81ea\u7531\u306b\u7bc4\u56f2\u306e\u78ba\u7387\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>&nbsp;<br 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