{"id":990,"date":"2020-06-08T11:00:00","date_gmt":"2020-06-08T02:00:00","guid":{"rendered":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/?p=990"},"modified":"2020-06-30T21:15:54","modified_gmt":"2020-06-30T12:15:54","slug":"probability-function","status":"publish","type":"post","link":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/probability-function","title":{"rendered":"\u78ba\u7387\u95a2\u6570\u30fb\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u3010\u9055\u3044\u3068\u610f\u5473\u3092\u89e3\u8aac\uff01\u3011"},"content":{"rendered":"\n<p class=\"has-text-align-right\"><span style=\"text-decoration: underline;\">\u5b66\u7fd2\u30ec\u30d9\u30eb\uff1a\u9ad8\u6821\u751f\u3000\u96e3\u6613\u5ea6\uff1a\u2605\u2606\u2606\u2606\u2606<\/span><\/p>\n\n\n\n\n\n\n\n<p>\u78ba\u7387\u5909\u6570\u304b\u3089\u78ba\u7387\u3092\u7d50\u3073\u3064\u3051\u308b\u305f\u3081\u306e\u95a2\u6570\u3092\u78ba\u7387\u5909\u6570\u30fb\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u3068\u3044\u3044\u307e\u3059\u3002\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u78ba\u7387\u95a2\u6570\u3068\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u306e\u9055\u3044\u3092\u8aac\u660e\u3057\u306a\u304c\u3089\u3001\u5177\u4f53\u4f8b\u3092\u4ea4\u3048\u3066\u89e3\u8aac\u3057\u3066\u3044\u304d\u305f\u3044\u3068\u601d\u3044\u307e\u3059\u3002\u5206\u5e03\u306e\u7279\u5fb4\u3092\u898b\u51fa\u3057\u305f\u308a\u3001\u7d71\u8a08\u7684\u306b\u63a8\u6e2c\u3059\u308b\u3068\u304d\u306b\u306f\u3001\u78ba\u7387\u95a2\u6570\u30fb\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u306e\u60c5\u5831\u306f\u5fc5\u9808\u306a\u306e\u3067\u3001\u3068\u3066\u3082\u6709\u610f\u7fa9\u306a\u8a18\u4e8b\u306b\u306a\u308b\u3068\u601d\u3044\u307e\u3059\u3088\uff01<\/p>\n\n\n\n<div id=\"toc_container\" class=\"toc_light_blue no_bullets\"><p class=\"toc_title\">\u76ee\u6b21<\/p><ul class=\"toc_list\"><li><a href=\"#i\"><span class=\"toc_number toc_depth_1\">1<\/span> \u78ba\u7387\u95a2\u6570\u30fb\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u3068\u306f<\/a><ul><li><a href=\"#i-2\"><span class=\"toc_number toc_depth_2\">1.1<\/span> \u96e2\u6563\u578b\u306e\u5834\u5408<\/a><\/li><li><a href=\"#i-3\"><span class=\"toc_number toc_depth_2\">1.2<\/span> \u9023\u7d9a\u578b\u306e\u5834\u5408<\/a><\/li><\/ul><\/li><li><a href=\"#i-4\"><span class=\"toc_number toc_depth_1\">2<\/span> \u5177\u4f53\u4f8b<\/a><\/li><li><a href=\"#i-5\"><span class=\"toc_number toc_depth_1\">3<\/span> \u78ba\u7387\u95a2\u6570\u30fb\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u306e\u307e\u3068\u3081<\/a><\/li><\/ul><\/div>\n<h2><span id=\"i\">\u78ba\u7387\u95a2\u6570\u30fb\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u3068\u306f<\/span><\/h2>\n\n\n\n<div style=\"display: inline-block; background: #33cc33; padding: 5px 10px; color: #ffffff; border-radius: 5px 5px 0 0;\"><strong>\u78ba\u7387\u95a2\u6570\u30fb\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570<\/strong><\/div>\n<div style=\"background: #ffffea; padding: 10px; border: 2px solid #33cc33;\">\u96e2\u6563\u578b\u306e\u78ba\u7387\u5909\u6570\u306e\u5024\u306b\u5bfe\u5fdc\u3059\u308b\u78ba\u7387\u3078\u7d50\u3073\u4ed8\u3051\u308b\u305f\u3081\u306e\u95a2\u6570\u3092\u78ba\u7387\u95a2\u6570\u3068\u3044\u3044\u307e\u3059\u3002\n\u540c\u69d8\u306b\u3001\u9023\u7d9a\u578b\u306e\u78ba\u7387\u5909\u6570\u306e\u5834\u5408\u306f\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u3068\u3044\u3044\u307e\u3059\u3002<\/div>\n<div>&nbsp;<\/div>\n\n\n\n<p>\u203b\u3000\u78ba\u7387\u5909\u6570\u306b\u3064\u3044\u3066\u306f<a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/random-variable\">\uff1c\u78ba\u7387\u5909\u6570\u306e\u8a18\u4e8b\uff1e<\/a>\u3092\u3054\u89a7\u304f\u3060\u3055\u3044\u30fb<br>\u203b\u3000\u96e2\u6563\u578b\u30fb\u9023\u7d9a\u578b\u306b\u3064\u3044\u3066\u306f<a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/discrete-continuous\">\uff1c\u96e2\u6563\u578b\u3068\u9023\u7d9a\u578b\u306e\u8a18\u4e8b\uff1e<\/a>\u3092\u3054\u89a7\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n<div class=\"wp-block-liquid-speech-balloon liquid-speech-balloon-wrap liquid-speech-balloon-00  liquid-speech-balloon-short\"><div class=\"liquid-speech-balloon-avatar\"><\/div><div class=\"liquid-speech-balloon-text\" style=\"border-color:#d6ebf8;background-color:#d6ebf8;color:#000000\"><p>\u78ba\u7387\u95a2\u6570\u3068\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u306e\u9055\u3044\u306f\u30c7\u30fc\u30bf\u304c\u96e2\u6563\u578b\u304b\u9023\u7d9a\u578b\u304b\u3060\u3051\u306e\u9055\u3044\u3067\u3059\u3002\u78ba\u7387\u95a2\u6570\u3068\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u305d\u308c\u305e\u308c\u306e\u6027\u8cea\u3092\u898b\u3066\u307f\u307e\u3057\u3087\u3046\uff01<\/p><div class=\"liquid-speech-balloon-arrow\" style=\"border-color:transparent #d6ebf8 transparent transparent\"><\/div><\/div><\/div>\n\n\n\n<h3><span id=\"i-2\">\u96e2\u6563\u578b\u306e\u5834\u5408<\/span><\/h3>\n\n\n\n<p>\u96e2\u6563\u578b\u306e\u78ba\u7387\u5909\u6570\\(X\\)\u306e\u53d6\u308a\u3046\u308b\u5024\u3092\\(\\{x_{1},x_{2},\\cdots\\}\\)\u3068\u3057\u307e\u3059\u3002\\(x_{i}\\)\u306b\u5bfe\u5fdc\u3059\u308b\u78ba\u7387\u3092\\(f(x_{i})\\)\u3068\u3057\u307e\u3059\u3002\u307e\u305a\u78ba\u7387\u306e\u516c\u7406\u304b\u3089<\/p>\n\n\n\n<ul><li>\\(0\\leq f(x_{i})\\leq 1\\)<\/li><li>\\(\\displaystyle\\sum_{i=1}^{\\infty}f(x_{i})=1\\)<\/li><\/ul>\n\n\n\n<p>\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n\n\n\n<div class=\"wp-block-liquid-speech-balloon liquid-speech-balloon-wrap liquid-speech-balloon-00  liquid-speech-balloon-short\"><div class=\"liquid-speech-balloon-avatar\"><\/div><div class=\"liquid-speech-balloon-text\" style=\"border-color:#d6ebf8;background-color:#d6ebf8;color:#000000\"><p>\u96e2\u6563\u578b\u306e\u5834\u5408\u306f\u3001\u78ba\u7387\u95a2\u6570\u306f\u3068\u3066\u3082\u5206\u304b\u308a\u3084\u3059\u3044\u3067\u3059\u3002<br>\u307e\u305a\u3001<strong>\u78ba\u7387\u95a2\u6570\uff08\u78ba\u7387\uff09\u306f\\(0\\)\u304b\u3089\\(1\\)\u306e\u9593\u306e\u5024\u3092\u3068\u308a\u307e\u3059<\/strong>\u3002\u305d\u3057\u3066\u3001<strong>\u5168\u3066\u306e\u5834\u5408\u306e\u78ba\u7387\u3092\u8db3\u3057\u5408\u308f\u305b\u308b\u3068\\(1\\)\u3068\u306a\u308a\u307e\u3059<\/strong>\u3002<\/p><div class=\"liquid-speech-balloon-arrow\" style=\"border-color:transparent #d6ebf8 transparent transparent\"><\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-liquid-speech-balloon liquid-speech-balloon-wrap liquid-speech-balloon-01 liquid-speech-balloon-right  liquid-speech-balloon-short\"><div class=\"liquid-speech-balloon-avatar\"><\/div><div class=\"liquid-speech-balloon-text\" style=\"border-color:#f4d379;background-color:#f4d379;color:#000000\"><p>\u9023\u7d9a\u578b\u3082\u540c\u3058\u3067\u306f\u306a\u306e\u3067\u3059\u304b\uff1f<\/p><div class=\"liquid-speech-balloon-arrow\" style=\"border-color:transparent transparent transparent #f4d379\"><\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-liquid-speech-balloon liquid-speech-balloon-wrap liquid-speech-balloon-00  liquid-speech-balloon-short\"><div class=\"liquid-speech-balloon-avatar\"><\/div><div class=\"liquid-speech-balloon-text\" style=\"border-color:#d6ebf8;background-color:#d6ebf8;color:#000000\"><p>\u5b9f\u306f\u9023\u7d9a\u578b\u306e\u5834\u5408\u3067\u306f\u5168\u7136\u7570\u306a\u308a\u307e\u3059\u3002<\/p><div class=\"liquid-speech-balloon-arrow\" style=\"border-color:transparent #d6ebf8 transparent transparent\"><\/div><\/div><\/div>\n\n\n\n<h3><span id=\"i-3\">\u9023\u7d9a\u578b\u306e\u5834\u5408<\/span><\/h3>\n\n\n\n<p>\u9023\u7d9a\u578b\u306e\u78ba\u7387\u5909\u6570\u306b\u5bfe\u3057\u3066\u30011\u70b9\u3067\u306e\u78ba\u7387\u306b\u610f\u5473\u304c\u306a\u3044\u3053\u3068\u306f<a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/discrete-continuous\">\uff1c\u96e2\u6563\u578b\u3068\u9023\u7d9a\u578b\u306e\u8a18\u4e8b\uff1e<\/a>\u3067\u8aac\u660e\u3057\u307e\u3057\u305f\u3002\u9023\u7d9a\u578b\u306e\u78ba\u7387\u5909\u6570\u3067\u78ba\u7387\u3092\u4e0e\u3048\u308b\u305f\u3081\u306b\u306f\u3001\u78ba\u7387\u5909\u6570\u306e\u7bc4\u56f2\u3067\u4e0e\u3048\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u9023\u7d9a\u578b\u306e\u78ba\u7387\u5909\u6570\\(X\\)\u306b\u5bfe\u5fdc\u3059\u308b\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u3092\\(f(x)\\)\u3068\u3057\u307e\u3059\u3002\u3053\u306e\u3068\u304d\u78ba\u7387\u5909\u6570\\(X\\)\u304c\u533a\u9593\\([a,b]\\)\u306e\u5024\u3092\u3068\u308b\u78ba\u7387\u306f$$\\mathrm{P}(a\\leq X\\leq b)=\\int_{b}^{a}f(x)dx$$\u3067\u5b9a\u7fa9\u3057\u307e\u3059\u3002\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u306f\u5fc5\u305a$$f(x)\\geq 0$$\u3068\u306a\u308a\u307e\u3059\u3002\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u306f\u78ba\u7387\u306e\u516c\u7406\u304b\u3089$$\\int_{-\\infty}^{\\infty}f(x)dx=1$$\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n\n\n\n<div class=\"wp-block-liquid-speech-balloon liquid-speech-balloon-wrap liquid-speech-balloon-00  liquid-speech-balloon-short\"><div class=\"liquid-speech-balloon-avatar\"><\/div><div class=\"liquid-speech-balloon-text\" style=\"border-color:#d6ebf8;background-color:#d6ebf8;color:#000000\"><p>\u3053\u306e\u3068\u304d\u6ce8\u610f\u3057\u306a\u3044\u3068\u3044\u3051\u306a\u3044\u3053\u3068\u306f\u3001<br>\u78ba\u7387\u95a2\u6570\u3068\u7570\u306a\u308a\u3001<strong>\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\\(f(x)\\)\u306f\\(1\\)\u4ee5\u4e0a\u306e\u5024\u3092\u3068\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002<\/strong>\u3053\u308c\u306f\u78ba\u7387\u3092\u7a4d\u5206\u306b\u3088\u308b\u9762\u7a4d\u3067\u4e0e\u3048\u3066\u3044\u308b\u3053\u3068\u306b\u7531\u6765\u3057\u307e\u3059\u3002<\/p><div class=\"liquid-speech-balloon-arrow\" style=\"border-color:transparent #d6ebf8 transparent transparent\"><\/div><\/div><\/div>\n\n\n\n<h2><span id=\"i-4\">\u5177\u4f53\u4f8b<\/span><\/h2>\n\n\n\n<p>\u3053\u306e\u8a18\u4e8b\u3067\u306f\u96e2\u6563\u578b\u306e\u78ba\u7387\u95a2\u6570\u3092\u7d39\u4ecb\u3057\u307e\u3059\u3002\u30b5\u30a4\u30b3\u30ed\u3092\u8003\u3048\u307e\u3059\u3002\u30b5\u30a4\u30b3\u30ed\u306e\u53d6\u308a\u3046\u308b\u5024\u306f\\(\\{x_{1}=1,x_{2}=2,x_{3}=3,x_{4}=4,x_{5}=5,x_{6}=6\\}\\)\u3068\u306a\u308a\u307e\u3059\u3002\u3053\u306e\u3068\u304d\u78ba\u7387\u95a2\u6570\u306f$$f(x_{i})=\\frac{1}{6}\\ \\ \\ \\ (i=1,\\cdots,6)$$\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<h2><span id=\"i-5\">\u78ba\u7387\u95a2\u6570\u30fb\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u306e\u307e\u3068\u3081<\/span><\/h2>\n\n\n\n<p>\u96e2\u6563\u578b\u306e\u78ba\u7387\u5909\u6570\u3068\u78ba\u7387\u3092\u7d50\u3073\u3064\u3051\u308b\u95a2\u6570\u3092\u78ba\u7387\u95a2\u6570\u3068\u3044\u3044\u3001\u9023\u7d9a\u578b\u306e\u78ba\u7387\u5909\u6570\u306e\u5834\u5408\u306f\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u3092\u3044\u3044\u307e\u3059\u3002\u96e2\u6563\u578b\u30fb\u9023\u7d9a\u578b\u305d\u308c\u305e\u308c\u3067\u78ba\u7387\u306b\u5bfe\u3059\u308b\u8003\u3048\u65b9\u304c\u7570\u306a\u308b\u3053\u3068\u304b\u3089\u3001\u78ba\u7387\u95a2\u6570\u3068\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u3067\u306f\u5fae\u5999\u306b\u6027\u8cea\u304c\u7570\u306a\u308a\u307e\u3059\u3002\u3069\u3061\u3089\u3082\u3001\u5168\u78ba\u7387\u5909\u6570\u306e\u78ba\u7387\u306f\\(1\\)\u306b\u306a\u308a\u307e\u3059\u304c\u3001\u78ba\u7387\u95a2\u6570\u306f\\(0\\)\u304b\u3089\\(1\\)\u306e\u5024\u3092\u3001\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u306f\\(0\\)\u4ee5\u4e0a\u306e\u5024\u3092\u3068\u308a\u307e\u3059\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5b66\u7fd2\u30ec\u30d9\u30eb\uff1a\u9ad8\u6821\u751f\u3000\u96e3\u6613\u5ea6\uff1a\u2605\u2606\u2606\u2606\u2606 \u78ba\u7387\u5909\u6570\u304b\u3089\u78ba\u7387\u3092\u7d50\u3073\u3064\u3051\u308b\u305f\u3081\u306e\u95a2\u6570\u3092\u78ba\u7387\u5909\u6570\u30fb\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u3068\u3044\u3044\u307e\u3059\u3002\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u78ba\u7387\u95a2\u6570\u3068\u78ba &#8230; <\/p>\n","protected":false},"author":1,"featured_media":829,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[54],"tags":[55,69,68],"jetpack_featured_media_url":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/05\/135-money-images.jpg","_links":{"self":[{"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts\/990"}],"collection":[{"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/comments?post=990"}],"version-history":[{"count":13,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts\/990\/revisions"}],"predecessor-version":[{"id":1846,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts\/990\/revisions\/1846"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/media\/829"}],"wp:attachment":[{"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/media?parent=990"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/categories?post=990"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/tags?post=990"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}