{"id":224,"date":"2023-08-03T23:08:41","date_gmt":"2023-08-03T23:08:41","guid":{"rendered":"https:\/\/statorials.org\/ja\/%e4%b8%80%e6%a7%98%e9%80%a3%e7%b6%9a%e5%88%86%e5%b8%83\/"},"modified":"2023-08-03T23:08:41","modified_gmt":"2023-08-03T23:08:41","slug":"%e4%b8%80%e6%a7%98%e9%80%a3%e7%b6%9a%e5%88%86%e5%b8%83","status":"publish","type":"post","link":"https:\/\/statorials.org\/ja\/%e4%b8%80%e6%a7%98%e9%80%a3%e7%b6%9a%e5%88%86%e5%b8%83\/","title":{"rendered":"\u5747\u4e00\u304b\u3064\u9023\u7d9a\u7684\u306a\u5206\u5e03"},"content":{"rendered":"<p>\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u9023\u7d9a\u4e00\u69d8\u5206\u5e03\u3068\u306f\u4f55\u304b\u3001\u307e\u305f\u305d\u308c\u304c\u4f55\u306b\u4f7f\u7528\u3055\u308c\u308b\u306e\u304b\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002\u9023\u7d9a\u4e00\u69d8\u5206\u5e03\u306e\u30b0\u30e9\u30d5\u3068\u3053\u306e\u30bf\u30a4\u30d7\u306e\u5206\u5e03\u306e\u7279\u6027\u3082\u8868\u793a\u3055\u308c\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-distribucion-uniforme-continua\"><\/span>\u9023\u7d9a\u4e00\u69d8\u5206\u5e03\u3068\u306f\u4f55\u3067\u3059\u304b?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u9023\u7d9a\u4e00\u69d8\u5206\u5e03\u306f\u3001<\/strong>\u3059\u3079\u3066\u306e\u5024\u304c\u540c\u3058\u767a\u751f\u78ba\u7387\u3092\u6301\u3064\u78ba\u7387\u5206\u5e03\u306e\u4e00\u7a2e\u3067\u3059\u3002\u63db\u8a00\u3059\u308c\u3070\u3001\u9023\u7d9a\u4e00\u69d8\u5206\u5e03\u3068\u306f\u3001\u78ba\u7387\u304c\u533a\u9593\u306b\u308f\u305f\u3063\u3066\u4e00\u69d8\u306b\u5206\u5e03\u3059\u308b\u5206\u5e03\u3067\u3042\u308b\u3002<\/p>\n<p>\u9023\u7d9a\u4e00\u69d8\u5206\u5e03\u306f\u3001\u78ba\u7387\u304c\u4e00\u5b9a\u3067\u3042\u308b\u9023\u7d9a\u5909\u6570\u3092\u8a18\u8ff0\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u540c\u69d8\u306b\u3001\u3059\u3079\u3066\u306e\u7d50\u679c\u304c\u540c\u3058\u78ba\u7387\u3092\u6301\u3064\u5834\u5408\u3001\u7d50\u679c\u306b\u30e9\u30f3\u30c0\u30e0\u6027\u304c\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3059\u308b\u305f\u3081\u3001\u9023\u7d9a\u4e00\u69d8\u5206\u5e03\u306f\u30e9\u30f3\u30c0\u30e0 \u30d7\u30ed\u30bb\u30b9\u3092\u5b9a\u7fa9\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002<\/p>\n<p>\u9023\u7d9a\u4e00\u69d8\u5206\u5e03\u306b\u306f\u3001\u7b49\u78ba\u7387\u533a\u9593\u3092\u5b9a\u7fa9\u3059\u308b 2 \u3064\u306e\u7279\u6027\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc<em>a<\/em>\u3068<em>b<\/em>\u304c\u3042\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u9023\u7d9a\u4e00\u69d8\u5206\u5e03\u306e\u8a18\u53f7\u306f<em>U(a,b)<\/em>\u3067\u3059\u3002\u3053\u3053\u3067\u3001 <em>a<\/em>\u3068<em>b<\/em>\u306f\u5206\u5e03\u306e\u7279\u6027\u5024\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-339036da3788f71282d3936dd092730c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim U(a,b)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"92\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u305f\u3068\u3048\u3070\u3001\u30e9\u30f3\u30c0\u30e0\u306a\u5b9f\u9a13\u306e\u7d50\u679c\u304c 5 \u304b\u3089 9 \u307e\u3067\u306e\u4efb\u610f\u306e\u5024\u3092\u3068\u308a\u3001\u8003\u3048\u3089\u308c\u308b\u3059\u3079\u3066\u306e\u7d50\u679c\u304c\u540c\u3058\u78ba\u7387\u3067\u767a\u751f\u3059\u308b\u5834\u5408\u3001\u5b9f\u9a13\u306f\u9023\u7d9a\u4e00\u69d8\u5206\u5e03 U(5.9) \u3067\u30b7\u30df\u30e5\u30ec\u30fc\u30c8\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u9023\u7d9a\u4e00\u69d8\u5206\u5e03\u306f\u3001<strong>\u9577\u65b9\u5f62\u5206\u5e03<\/strong>\u3068\u3082\u547c\u3070\u308c\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-distribucion-uniforme-continua\"><\/span>\u9023\u7d9a\u5747\u4e00\u5206\u5e03\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e00\u69d8\u5206\u5e03\u306e\u78ba\u7387\u3092\u5b9a\u7fa9\u3059\u308b\u5bc6\u5ea6\u95a2\u6570\u306f\u3001 <em>b<\/em>\u3068<em>a<\/em>\u306e\u5dee\u3067\u5272\u3063\u305f\u3082\u306e\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001<strong>\u9023\u7d9a\u4e00\u69d8\u5206\u5e03\u306e\u516c\u5f0f\u306f\u6b21<\/strong>\u306e\u3088\u3046\u306b\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-f28c4a144fb1377061b84b56968c9540_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}X\\sim U(a,b)\\\\[2ex]f(x)=\\cfrac{1}{b-a}\\\\[4ex]x\\in [a,b]\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"123\" width=\"99\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u4e00\u65b9\u3001\u9023\u7d9a\u4e00\u69d8\u5206\u5e03\u306e\u7d2f\u7a4d\u78ba\u7387\u95a2\u6570\u306f\u6b21\u306e\u5f0f\u3067\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002<\/p>\n<pre class=\"ql-errors\"> *** QuickLaTeX cannot compile formula:\n\\displaystyle F(x)=\\left\\{\\begin{array}{ll}0&amp;\\text{si }x&lt;h2 class=\"wp-block-heading\"&gt;&lt;span class=\"ez-toc-section\" id =\"grafica-de-la-distribucion-uniforme-continua\"&gt;&lt;\/span&gt; Graph of continuous uniform distribution&lt;span class=\"ez-toc-section-end\"&gt;&lt;\/span&gt;&lt;\/h2&gt; Since in a distribution uniform continuous probability is constant, its graphical representation is simply a function with a constant value defined in the same interval as the uniform distribution. &lt;figure class=\"wp-block-image aligncenter size-full is-resized\"&gt;&lt;img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/ 08\/distribution-uniforme-continue.png\" alt=\"Continuous uniform distribution graph\" class=\"wp-image-4498\" width=\"330\" height=\"232\" srcset=\"\" sizes=\"\"&gt;&lt;\/figure &gt; On the other hand, the cumulative probability graph of the continuous uniform distribution is as follows: &lt;figure class=\"wp-block-image aligncenter size-full is-resized\"&gt;&lt;img decoding=\"async\" loading=\"lazy \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/distribution-uniforme-continue-probabilite-cumulative.png\" alt=\"cumulative probability plot of a continuous uniform distribution\" class= \"wp-image-4499\" width=\"247\" height=\"193\" srcset=\"\" sizes=\"\"&gt;&lt;\/figure&gt;&lt;h2 class=\"wp-block-heading\"&gt;&lt;span class=\"ez-toc -section\" id=\"caracteristicas-de-la-distribucion-uniforme-continua\"&gt;&lt;\/span&gt; Characteristics of the continuous uniform distribution&lt;span class=\"ez-toc-section-end\"&gt;&lt;\/span&gt;&lt;\/h2 &gt; The continuous uniform distribution has the following characteristics: &lt;ul&gt;&lt;li&gt; The continuous uniform distribution is defined by two real parameters, &lt;em&gt;a&lt;\/em&gt; and &lt;em&gt;b&lt;\/em&gt;, which establish the limits in which the probability is constant.&lt;\/li&gt;&lt;\/ul&gt;[latex]a,b\\in \\mathbb{R}\n\n***Error message:\nPlease use \\mathaccent for accents in math mode.\nleading text: ...continuous uniform distribution probability\nPlease use \\mathaccent for accents in math mode.\nleading text: ...if the probability is constant, its representation\nPlease use \\mathaccent for accents in math mode.\nleading text: ...a function with a constant value de\nPlease use \\mathaccent for accents in math mode.\nleading text: ...c a constant value defined in the same\nPlease use \\mathaccent for accents in math mode.\nleading text: ...On the other hand, the probability graph\nPlease use \\mathaccent for accents in math mode.\nleading text: ... part, the cumulative probability graph\nPlease use \\mathaccent for accents in math mode.\nleading text: ...nue-probabilite-cumulative.png\" alt=\"plot\n\n<\/pre>\n<ul>\n<li>\u9023\u7d9a\u4e00\u69d8\u5206\u5e03\u306f\u3001 <em>a<\/em>\u3068<em>b<\/em>\u3092\u542b\u3080\u533a\u9593\u5185\u306b\u4f4d\u7f6e\u3059\u308b\u5024\u306e\u307f\u3092\u53d6\u308b\u3053\u3068\u304c\u3067\u304d\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-3d713e1ad32e4d969c10e514cd71b7d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\\in [a,b]\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u9023\u7d9a\u4e00\u69d8\u5206\u5e03\u306e\u5e73\u5747\u306f\u3001\u305d\u306e 2 \u3064\u306e\u7279\u6027\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u306e\u5408\u8a08\u3092 2 \u3067\u5272\u3063\u305f\u3082\u306e\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-96d92a77b5dce5d38b2b2f3b79ac09a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"E[X]=\\cfrac{a+b}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"105\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<ul>\n<li>\u9023\u7d9a\u4e00\u69d8\u5206\u5e03\u306e\u5206\u6563\u306f\u3001 <em>b<\/em>\u3068<em>a<\/em>\u306e\u5dee\u306e 2 \u4e57\u3092 12 \u3067\u5272\u3063\u305f\u3082\u306e\u306b\u76f8\u5f53\u3057\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-1f52c10cdd7fb59fca29f8d7703e7495_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Var(X)=\\cfrac{(b-a)^2}{12}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"149\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<ul>\n<li>\u9023\u7d9a\u4e00\u69d8\u5206\u5e03\u306e\u4e2d\u592e\u5024\u306f\u5e73\u5747\u5024\u3068\u4e00\u81f4\u3059\u308b\u305f\u3081\u3001\u540c\u3058\u5f0f\u3092\u4f7f\u7528\u3057\u3066\u8a08\u7b97\u3055\u308c\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-9acd8c7117f5765f6e47060148e541e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Me=\\cfrac{a+b}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"92\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<ul>\n<li>\u9023\u7d9a\u4e00\u69d8\u5206\u5e03\u306f\u5bfe\u79f0\u3067\u3042\u308b\u305f\u3081\u3001\u3053\u306e\u30bf\u30a4\u30d7\u306e\u5206\u5e03\u306e\u975e\u5bfe\u79f0\u4fc2\u6570\u306f\u30bc\u30ed\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-f32c2fb2ba717dc1c88c67cb82c26e9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A=0\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"46\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li>\u9023\u7d9a\u4e00\u69d8\u5206\u5e03\u306e\u5c16\u5ea6\u306f\u30d1\u30e9\u30e1\u30fc\u30bf\u306b\u4f9d\u5b58\u305b\u305a\u3001\u5e38\u306b -6 \u3092 5 \u3067\u5272\u3063\u305f\u5024\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-53318cb30ff0697fd742850c405c7545_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C=\\cfrac{-6}{5}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"71\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<ul>\n<li>\u6a19\u6e96\u4e00\u69d8\u5206\u5e03\u306f\u3001\u30d1\u30e9\u30e1\u30fc\u30bf<em>a<\/em>\u3068<em>b<\/em>\u304c\u305d\u308c\u305e\u308c 0 \u3068 1 \u3067\u3042\u308b\u9023\u7d9a\u4e00\u69d8\u5206\u5e03\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-be2dbf7d29ed8c8a1220e74498c77d6d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim U(0,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"92\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"distribucion-uniforme-continua-y-distribucion-uniforme-discreta\"><\/span>\u9023\u7d9a\u4e00\u69d8\u5206\u5e03\u3068\u96e2\u6563\u4e00\u69d8\u5206\u5e03<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6700\u5f8c\u306b\u3001\u9023\u7d9a\u4e00\u69d8\u5206\u5e03\u3068\u96e2\u6563\u4e00\u69d8\u5206\u5e03\u306e\u9055\u3044\u3092\u898b\u3066\u3044\u304d\u307e\u3059\u3002\u3053\u308c\u3089\u306f\u6df7\u540c\u3055\u308c\u308b\u53ef\u80fd\u6027\u304c\u3042\u308b 2 \u3064\u306e\u78ba\u7387\u5206\u5e03\u3067\u3059\u304c\u3001\u307e\u3063\u305f\u304f\u7570\u306a\u308b\u6982\u5ff5\u3092\u8868\u3057\u3066\u3044\u308b\u305f\u3081\u3067\u3059\u3002<\/p>\n<p><strong>\u9023\u7d9a\u4e00\u69d8\u5206\u5e03\u3068\u96e2\u6563\u4e00\u69d8\u5206\u5e03\u306e\u4e3b\u306a\u9055\u3044\u306f\u3001<\/strong>\u53d6\u308a\u5f97\u308b\u5024\u3067\u3059\u3002\u9023\u7d9a\u7684\u306a\u4e00\u69d8\u5206\u5e03\u306f\u9023\u7d9a\u7684\u306a\u30b5\u30f3\u30d7\u30eb\u7a7a\u9593\u3067\u5b9a\u7fa9\u3055\u308c\u3001\u96e2\u6563\u7684\u306a\u4e00\u69d8\u5206\u5e03\u306f\u96e2\u6563\u7684\u306a\u30b5\u30f3\u30d7\u30eb\u7a7a\u9593\u3067\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u96e2\u6563\u4e00\u69d8\u5206\u5e03\u306f\u533a\u9593\u5185\u3067\u5c11\u6570\u306e\u5024 (\u901a\u5e38\u306f\u6574\u6570) 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href=\"https:\/\/statorials.org\/ja\/\u96e2\u6563\u4e00\u69d8\u5206\u5e03\/\">\u96e2\u6563\u4e00\u69d8\u5206\u5e03<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u9023\u7d9a\u4e00\u69d8\u5206\u5e03\u3068\u306f\u4f55\u304b\u3001\u307e\u305f\u305d\u308c\u304c\u4f55\u306b\u4f7f\u7528\u3055\u308c\u308b\u306e\u304b\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002\u9023\u7d9a\u4e00\u69d8\u5206\u5e03\u306e\u30b0\u30e9\u30d5\u3068\u3053\u306e\u30bf\u30a4\u30d7\u306e\u5206\u5e03\u306e\u7279\u6027\u3082\u8868\u793a\u3055\u308c\u307e\u3059\u3002 \u9023\u7d9a\u4e00\u69d8\u5206\u5e03\u3068\u306f\u4f55\u3067\u3059\u304b? \u9023\u7d9a\u4e00\u69d8\u5206\u5e03\u306f\u3001\u3059\u3079\u3066\u306e\u5024\u304c\u540c\u3058\u767a\u751f\u78ba\u7387\u3092\u6301\u3064 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