{"id":107,"date":"2023-08-05T09:10:02","date_gmt":"2023-08-05T09:10:02","guid":{"rendered":"https:\/\/statorials.org\/ja\/%e5%88%86%e5%b8%83%e9%96%a2%e6%95%b0\/"},"modified":"2023-08-05T09:10:02","modified_gmt":"2023-08-05T09:10:02","slug":"%e5%88%86%e5%b8%83%e9%96%a2%e6%95%b0","status":"publish","type":"post","link":"https:\/\/statorials.org\/ja\/%e5%88%86%e5%b8%83%e9%96%a2%e6%95%b0\/","title":{"rendered":"\u5206\u5e03\u95a2\u6570"},"content":{"rendered":"<p>\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u5206\u5e03\u95a2\u6570\u306e\u8aac\u660e\u3001\u305d\u306e\u5024\u306e\u8a08\u7b97\u65b9\u6cd5\u3001\u304a\u3088\u3073\u5206\u5e03\u95a2\u6570\u306e\u5b9f\u969b\u306e\u4f8b\u3092\u793a\u3057\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u5206\u5e03\u95a2\u6570\u3068\u5bc6\u5ea6\u95a2\u6570\u306e\u9055\u3044\u3082\u78ba\u8a8d\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-funcion-de-distribucion\"><\/span>\u5206\u914d\u95a2\u6570\u3068\u306f\u4f55\u3067\u3059\u304b?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u5206\u5e03\u95a2\u6570 \u306f<\/strong>\u3001<strong>\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570<\/strong>\u3068\u3082\u547c\u3070\u308c\u3001\u5206\u5e03\u306e\u7d2f\u7a4d\u78ba\u7387\u3092\u793a\u3059\u6570\u5b66\u95a2\u6570\u3067\u3059\u3002\u3064\u307e\u308a\u3001\u4efb\u610f\u306e\u5024\u306e\u5206\u5e03\u95a2\u6570\u306e\u30a4\u30e1\u30fc\u30b8\u306f\u3001\u5909\u6570\u304c\u305d\u306e\u5024\u307e\u305f\u306f\u305d\u308c\u3088\u308a\u4f4e\u3044\u5024\u3092\u53d6\u308b\u78ba\u7387\u306b\u7b49\u3057\u304f\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\u306f\u982d\u5b57\u8a9e FDA \u3067\u547c\u3070\u308c\u308b\u3053\u3068\u3082\u3042\u308a\u307e\u3059\u304c\u3001\u901a\u5e38\u306e\u8a18\u53f7\u306f\u5927\u6587\u5b57\u306e F \u3067\u3059\u3002<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u5206\u5e03\u95a2\u6570\u306f\u6b21\u306e\u5f0f\u3067\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-c8cf5efd36881f74974a11b10af2dd4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"F(x)=P[X\\leq x]\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"133\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-calcular-la-funcion-de-distribucion\"><\/span>\u5206\u5e03\u95a2\u6570\u306e\u8a08\u7b97\u65b9\u6cd5<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6b21\u306b\u3001\u78ba\u7387\u5206\u5e03\u304c\u96e2\u6563\u7684\u3067\u3042\u308b\u304b\u9023\u7d9a\u7684\u3067\u3042\u308b\u304b\u306b\u5fdc\u3058\u3066\u5206\u5e03\u95a2\u6570\u306e\u5024\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5\u3092\u8aac\u660e\u3057\u307e\u3059\u3002<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caso-discreto\"><\/span>\u79d8\u5bc6\u306e\u30dc\u30c3\u30af\u30b9<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u78ba\u7387\u5909\u6570\u304c\u96e2\u6563\u578b\u306e\u5834\u5408\u3001\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\u306f<em>x<\/em>\u4ee5\u4e0b\u306e\u3059\u3079\u3066\u306e\u5024\u306e\u78ba\u7387\u306e\u5408\u8a08\u306b\u7b49\u3057\u304f\u306a\u308a\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-c3b978075c7791d3379a8c170010eb2c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle F(x)=P[X\\leq x]=\\sum_{u\\leq x}f(u)\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"222\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p>\u91d1<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-5875573ff1b51b9b17fc81a368fabc07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(u)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"34\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u306f\u3001\u96e2\u6563\u5909\u6570\u306b\u95a2\u9023\u4ed8\u3051\u3089\u308c\u305f\u78ba\u7387\u95a2\u6570\u3067\u3059\u3002<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caso-continuo\"><\/span>\u7d99\u7d9a\u6848\u4ef6<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u78ba\u7387\u5909\u6570\u304c\u9023\u7d9a\u306e\u5834\u5408\u3001\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\u306f\u3001\u30de\u30a4\u30ca\u30b9\u7121\u9650\u5927\u304b\u3089\u554f\u984c\u306e\u5024\u307e\u3067\u306e\u5bc6\u5ea6\u95a2\u6570\u306e\u7a4d\u5206\u306b\u76f8\u5f53\u3057\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-36434a36d91add71ad209868965d6ccb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle F(x)=P[X\\leq x]=\\int_{-\\infty}^{x}f(u)du\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"250\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u91d1<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-5875573ff1b51b9b17fc81a368fabc07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(u)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"34\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u306f\u9023\u7d9a\u5909\u6570\u306b\u95a2\u9023\u4ed8\u3051\u3089\u308c\u305f\u5bc6\u5ea6\u95a2\u6570\u3067\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-la-funcion-de-distribucion\"><\/span>\u5206\u5e03\u95a2\u6570\u306e\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5206\u5e03\u95a2\u6570\u306e\u5b9a\u7fa9\u3092\u7406\u89e3\u3057\u305f\u3068\u3053\u308d\u3067\u3001\u5206\u5e03\u95a2\u6570\u306e\u5024\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5\u3092\u5b66\u3076\u305f\u3081\u306e\u5b9f\u8df5\u7684\u306a\u4f8b\u3092\u6bb5\u968e\u7684\u306b\u898b\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\u30b3\u30a4\u30f3\u3092 4 \u56de\u6295\u3052\u308b\u30e9\u30f3\u30c0\u30e0\u5b9f\u9a13\u306e\u5206\u5e03\u95a2\u6570\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/li>\n<\/ul>\n<p>\u3053\u306e\u6f14\u7fd2\u3092\u89e3\u304f\u306b\u306f\u3001\u307e\u305a 4 \u56de\u306e\u30b3\u30a4\u30f3\u6295\u3052\u3067\u5f97\u3089\u308c\u308b\u8868\u306e\u6570\u306b\u95a2\u9023\u3059\u308b\u3059\u3079\u3066\u306e\u78ba\u7387\u3092\u8a08\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002 <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/probabilite-lancer-quatre-pieces.png\" alt=\"4\u679a\u306e\u30b3\u30a4\u30f3\u3092\u6295\u3052\u308b\u78ba\u7387\" class=\"wp-image-2346\" width=\"492\" height=\"331\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u3053\u308c\u306f\u96e2\u6563\u5909\u6570\u3067\u3042\u308b\u305f\u3081\u3001\u5206\u5e03\u95a2\u6570\u306e\u30a4\u30e1\u30fc\u30b8\u3092\u6c7a\u5b9a\u3059\u308b\u306b\u306f\u3001\u554f\u984c\u306e\u5909\u6570\u306e\u5024\u307e\u3067\u78ba\u7387\u3092\u52a0\u7b97\u3059\u308b\u3060\u3051\u3067\u5341\u5206\u3067\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-63c3574be5cdcf6de8b54f910c01e35e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}F(X\\leq 0)=f(0)=0,0625\\\\[4ex]\\begin{aligned}F(X\\leq 1)&amp; =f(0)+f(1)\\\\[1.1ex] &amp; =0,0625+0,25=0,3125\\end{aligned}\\\\[6ex]\\begin{aligned}F(X\\leq 2)&amp; =f(0)+f(1)+f(2)\\\\[1.1ex] &amp; =0,0625+0,25+0,375=0,6875\\end{aligned}\\\\[6ex]\\begin{aligned}F(X\\leq 3)&amp; =f(0)+f(1)+f(2)+f(3)\\\\[1.1ex] &amp; =0,0625+0,25+0,375+0,25=0,9375\\end{aligned}\\\\[6ex]\\begin{aligned}F(X\\leq 4)&amp; =f(0)+f(1)+f(2)+f(3)+f(4)\\\\[1.1ex] &amp; =0,0625+0,25+0,375+0,25+0,0625=1\\end{aligned}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"363\" width=\"435\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u30014 \u3064\u306e\u72ec\u7acb\u3057\u305f\u30b3\u30a4\u30f3\u3092\u6295\u3052\u308b\u3053\u3068\u306b\u3088\u308b\u8868\u5411\u304d\u306e\u5206\u5e03\u95a2\u6570\u306e\u5024\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/probabilite-cumulative-lancer-quatre-pieces.png\" alt=\"\" class=\"wp-image-2362\" width=\"224\" height=\"331\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"propiedades-de-la-funcion-de-distribucion\"><\/span>\u5206\u5e03\u95a2\u6570\u306e\u6027\u8cea<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5909\u6570\u306e\u30bf\u30a4\u30d7\u306b\u95a2\u4fc2\u306a\u304f\u3001\u5206\u5e03\u95a2\u6570\u306b\u306f\u5e38\u306b\u6b21\u306e\u30d7\u30ed\u30d1\u30c6\u30a3\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\u306e\u5024\u306f 0 \uff5e 1 \u3067\u3059\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-b43459e3f1bfcf6f783408bb57f2b823_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"0\\leq F(x) \\leq 1\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"102\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> <em>x \u304c<\/em>\u7121\u9650\u5927\u306b\u8fd1\u3065\u304f\u50be\u5411\u304c\u3042\u308b\u3068\u304d\u306e\u5206\u5e03\u95a2\u6570\u306e\u6975\u9650\u306f 1 \u306b\u7b49\u3057\u304f\u306a\u308a\u307e\u3059\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-18a8b8bd2a28b6e5bf66af92771f690e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to +\\infty} F(x)=1\" title=\"Rendered by QuickLaTeX.com\" height=\"27\" width=\"118\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<ul>\n<li>\u4e00\u65b9\u3001 <em>x \u304c<\/em>\u30de\u30a4\u30ca\u30b9\u7121\u9650\u5927\u306b\u8fd1\u3065\u304f\u3068\u304d\u306e\u5206\u5e03\u95a2\u6570\u306e\u6975\u9650\u306f\u30bc\u30ed\u306b\u306a\u308a\u307e\u3059\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-121e332e607371288d172844a59d5e8e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to -\\infty} F(x)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"119\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<ul>\n<li>\u305d\u306e\u7279\u6027\u306b\u3088\u308a\u3001\u5206\u5e03\u95a2\u6570\u306f\u5358\u8abf\u304b\u3064\u975e\u6e1b\u5c11\u3067\u3059\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-1b3f9780a83c58a6add1513c112f601b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x_1 \\leq x_2 \\implies F(x_1)\\leq F(x_2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"221\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u3055\u3089\u306b\u3001\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-42ce2269b42ed638b79b5c3e01e8d34c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\\leq b\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"41\" style=\"vertical-align: -3px;\"><\/p>\n<p>\u4ee5\u4e0b\u306e\u5f0f\u304c\u6210\u308a\u7acb\u3064\u3002 <\/li>\n<\/ul>\n<pre class=\"ql-errors\"> *** QuickLaTeX cannot compile formula:\n\\begin{array}{l}P(X &lt; a) = F(a^-)\\\\[2ex] P(X&gt;a)=1-F(a)\\\\[2ex]P(X \\ge a )=1-F(a^-)\\\\[2ex]P(a&lt;ul&gt;&lt;li&gt; Finally, if the statistical variable is continuous, the following equality is satisfied: &lt;\/li&gt;&lt;\/ul&gt;[latex ]\\begin{array}{l}P(a \\le X &lt; b) = \\displaystyle\\int_{a}^{b}f(x)\\,dx = F(b)- F(a)\\end{array}\n\n*** Error message:\nMissing $ inserted.\nleading text: \\begin{array}{l}\nPlease use \\mathaccent for accents in math mode.\nleading text: ... the statistical variable is continuous, the\nPlease use \\mathaccent for accents in math mode.\nleading text: ...iable statistic is continuous, equality\n\\begin{array} on input line 8 ended by \\end{document}.\nleading text: \\end{document}\nImproper \\prevdepth.\nleading text: \\end{document}\nMissing $ inserted.\nleading text: \\end{document}\nMissing } inserted.\nleading text: \\end{document}\nMissing \\cr inserted.\nleading text: \\end{document}\nMissing $ inserted.\nleading text: \\end{document}\nYou can't use `\\end' in internal vertical mode.\nleading text: \\end{document}\n\\begin{array} on input line 8 ended by \\end{document}.\nleading text: \\end{document}\n\n<\/pre>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"funcion-de-distribucion-y-funcion-de-densidad\"><\/span>\u5206\u5e03\u95a2\u6570\u3068\u5bc6\u5ea6\u95a2\u6570<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6700\u5f8c\u306b\u3001\u5206\u5e03\u95a2\u6570\u3068\u5bc6\u5ea6\u95a2\u6570\u306e\u9055\u3044\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002\u3053\u308c\u3089 2 \u3064\u306e\u7d71\u8a08\u6982\u5ff5\u306f\u6df7\u540c\u3055\u308c\u308b\u3053\u3068\u304c\u591a\u3044\u305f\u3081\u3067\u3059\u3002<\/p>\n<p><strong>\u5206\u5e03\u95a2\u6570\u3068\u5bc6\u5ea6\u95a2\u6570\u306e\u9055\u3044\u306f\u3001<\/strong>\u305d\u308c\u3089\u304c\u5b9a\u7fa9\u3059\u308b\u78ba\u7387\u306e\u30bf\u30a4\u30d7\u3067\u3059\u3002\u5bc6\u5ea6\u95a2\u6570\u306f\u5909\u6570\u304c\u7279\u5b9a\u306e\u5024\u3092\u53d6\u308b\u78ba\u7387\u3092\u8868\u3057\u3001\u5206\u5e03\u95a2\u6570\u306f\u5909\u6570\u306e\u7d2f\u7a4d\u78ba\u7387\u3092\u8868\u3057\u307e\u3059\u3002<\/p>\n<p>\u3064\u307e\u308a\u3001\u5206\u5e03\u95a2\u6570\u306f\u3001\u5909\u6570\u304c\u7279\u5b9a\u306e\u5024\u4ee5\u4e0b\u3067\u3042\u308b\u78ba\u7387\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002<\/p>\n<p>\u5bc6\u5ea6\u95a2\u6570\u306f\u9023\u7d9a\u5909\u6570\u306e\u307f\u3092\u53c2\u7167\u3059\u308b\u305f\u3081\u3001\u3053\u306e\u533a\u5225\u306f\u8abf\u67fb\u5bfe\u8c61\u306e\u5909\u6570\u304c\u9023\u7d9a\u5909\u6570\u3067\u3042\u308b\u5834\u5408\u306b\u306e\u307f\u610f\u5473\u304c\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n<p>\u5e73\u5747 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