{"id":107479,"date":"2024-08-17T01:22:54","date_gmt":"2024-08-17T01:22:54","guid":{"rendered":"https:\/\/science-hub.click\/%E7%8B%AC%E7%AB%8B%E6%80%A7%28%E7%A2%BA%E7%8E%87%29%E3%81%AB%E3%81%A4%E3%81%84%E3%81%A6%E8%A9%B3%E3%81%97%E3%81%8F%E8%A7%A3%E8%AA%AC\/"},"modified":"2024-08-17T01:22:54","modified_gmt":"2024-08-17T01:22:54","slug":"%E7%8B%AC%E7%AB%8B%E6%80%A7%28%E7%A2%BA%E7%8E%87%29%E3%81%AB%E3%81%A4%E3%81%84%E3%81%A6%E8%A9%B3%E3%81%97%E3%81%8F%E8%A7%A3%E8%AA%AC","status":"publish","type":"post","link":"https:\/\/science-hub.click\/?p=107479","title":{"rendered":"\u72ec\u7acb\u6027 (\u78ba\u7387)\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac"},"content":{"rendered":"<div><div><h2>\u5c0e\u5165<\/h2><p><b>\u72ec\u7acb\u6027<\/b>\u3068\u306f\u3001\u76f8\u4e92\u306b\u5f71\u97ff\u3092\u53ca\u307c\u3055\u306a\u3044\u30e9\u30f3\u30c0\u30e0\u306a\u30a4\u30d9\u30f3\u30c8\u3092\u76f4\u89b3\u7684\u306b\u8a8d\u5b9a\u3059\u308b\u78ba\u7387\u7684\u306a\u6982\u5ff5\u3067\u3059\u3002\u3053\u308c\u306f\u7d71\u8a08\u3084\u78ba\u7387\u8a08\u7b97\u306b\u304a\u3044\u3066\u975e\u5e38\u306b\u91cd\u8981\u306a\u6982\u5ff5\u3067\u3059\u3002<\/p><p>\u305f\u3068\u3048\u3070\u3001\u30b5\u30a4\u30b3\u30ed\u306e\u6700\u521d\u306e\u76ee\u306e\u5024\u306f\u30012 \u756a\u76ee\u306e\u76ee\u306e\u5024\u306b\u306f\u5f71\u97ff\u3057\u307e\u305b\u3093\u3002\u540c\u69d8\u306b\u3001<b>\u6295\u3052<\/b>\u306e\u5834\u5408\u3001 <i>4 \u4ee5\u4e0b\u306e\u5024\u3092\u53d6\u5f97\u3057\u3066\u3082<\/i>\u3001<i>\u7d50\u679c\u304c\u5076\u6570\u304b\u5947\u6570\u3067\u3042\u308b<\/i><span><a href=\"https:\/\/science-hub.click\/?p=57009\">\u78ba\u7387<\/a><\/span>\u306b\u306f\u5f71\u97ff\u3057\u307e\u305b\u3093\u30022 \u3064\u306e\u30a4\u30d9\u30f3\u30c8\u306f<i>\u72ec\u7acb\u3057\u3066\u3044\u308b<\/i>\u3068\u8a00\u308f\u308c\u307e\u3059\u3002<\/p><p> 2 \u3064\u306e\u30a4\u30d9\u30f3\u30c8\u304c\u72ec\u7acb\u3057\u3066\u3044\u308b\u304b\u3069\u3046\u304b\u3092\u78ba\u7acb\u3059\u308b\u306e\u306f\u5fc5\u305a\u3057\u3082\u7c21\u5358\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/p><figure class=\"wp-block-image size-large is-style-default\">\n<img decoding=\"async\" alt=\"\u72ec\u7acb\u6027 (\u78ba\u7387)\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\" class=\"aligncenter\" onerror=\"this.style.display=none;\" src=\"https:\/\/img.youtube.com\/vi\/e_ZFra-5_RM\/0.jpg\" style=\"width:100%;\"\/><\/figure><h2> 2 \u3064\u306e\u30a4\u30d9\u30f3\u30c8\u306e\u72ec\u7acb\u6027<\/h2><p>2 \u3064\u306e\u30a4\u30d9\u30f3\u30c8\u306e\u72ec\u7acb\u6027\u306e\u6570\u5b66\u7684<span><a href=\"https:\/\/science-hub.click\/?p=74671\">\u5b9a\u7fa9<\/a><\/span>\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002<\/p><div><p><strong>\u5b9a\u7fa9<\/strong><span>&#8211;<\/span> A \u3068 B \u306f\u72ec\u7acb\u3057\u3066\u3044\u307e\u3059<div class=\"math-formual notranslate\">$$ { \\Leftrightarrow \\mathbb{P}(A \\cap B) = \\mathbb{P}(A) \\cdot \\mathbb{P}(B).} $$<\/div><\/p><\/div><p>\u4e0a\u8a18\u306e\u6570\u5b66\u7684\u5b9a\u7fa9\u306f\u3042\u307e\u308a\u610f\u5473\u304c\u3042\u308a\u307e\u305b\u3093\u3002<i>\u6761\u4ef6\u4ed8\u304d\u78ba\u7387<\/i>\u306e\u6982\u5ff5\u3092\u5c0e\u5165\u3059\u308b\u3068\u3001\u72ec\u7acb\u6027\u306e\u76f4\u89b3\u7684\u306a\u6982\u5ff5\u3068\u4e0a\u8a18\u306e\u300c\u7a4d\u306e\u516c\u5f0f\u300d\u306e\u9593\u306e\u3064\u306a\u304c\u308a\u304c\u3088\u308a\u660e\u78ba\u306b\u306a\u308a\u307e\u3059\u3002<\/p><div><p><strong>\u5b9a\u7fa9<\/strong><span>\u2014<\/span>\u3082\u3057<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ \\mathbb{P}(B) \\neq 0,} $$<\/div> <i>A \u304c<\/i><i>B \u3092<\/i>\u77e5\u3063\u3066\u3044\u308b<i>\u6761\u4ef6\u4ed8\u304d\u78ba\u7387<\/i>\u3002 <div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ \\mathbb{P}(A\\mid B),\\ } $$<\/div>\u306f\u4ee5\u4e0b\u306e\u95a2\u4fc2\u306b\u3088\u3063\u3066\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002 <\/p><center><div class=\"math-formual notranslate\">$$ {\\mathbb{P}(A\\mid B)={\\mathbb{P}(A \\cap B) \\over \\mathbb{P}(B)}.  } $$<\/div><\/center><\/div><p> <i>B<\/i>\u304c<i>\u4e0d\u53ef\u80fd<\/i>\u3067<i>B<\/i>\u304c<i>\u78ba\u5b9f\u3067<\/i>\u3042\u308b\u3068\u3044\u3046\u8208\u5473\u306e\u306a\u3044\u7279\u5b9a\u306e\u30b1\u30fc\u30b9\u3092\u9664\u5916\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u72ec\u7acb\u6027\u306e\u5b9a\u7fa9\u3092\u6b21\u306e\u3088\u3046\u306b\u518d\u5b9a\u5f0f\u5316\u3067\u304d\u307e\u3059\u3002<\/p><div><p><strong>\u5b9a\u7fa9<\/strong><span>\u2014<\/span> <i>B<\/i>\u306e\u78ba\u7387\u304c<b>0 \u3067\u3082 1 \u3067\u3082\u306a\u3044\u5834\u5408\u3001\u4ee5\u4e0b\u306e\u6761\u4ef6\u306e\u3044\u305a\u308c\u304b<\/b>(\u3059\u3079\u3066\u540c\u7b49) \u304c\u6e80\u305f\u3055\u308c\u308c\u3070\u3001 <i>A<\/i>\u3068<i>B<\/i>\u306f\u72ec\u7acb\u3057\u3066\u3044\u307e\u3059\u3002 <\/p><center><div class=\"math-formual notranslate\">$$ {\\begin{align}\\mathbb{P}(A\\mid B)\\ &amp;=\\ \\mathbb{P}(A),\\\\\\mathbb{P}(A\\mid \\overline{B})\\ &amp;=\\ \\mathbb{P}(A),\\\\\\mathbb{P}(A\\mid B)\\ &amp;=\\ \\mathbb{P}(A\\mid \\overline{B}).\\end{align}} $$<\/div><\/center><\/div><p>\u3057\u305f\u304c\u3063\u3066\u3001\u30a4\u30d9\u30f3\u30c8<i>A<\/i>\u306b\u5bfe\u3059\u308b\u4e88\u6e2c\u304c\u540c\u3058\u3067\u3042\u308c\u3070\u3001\u30a4\u30d9\u30f3\u30c8<i>A<\/i>\u3068<i>B<\/i>\u306f\u72ec\u7acb\u3057\u3066\u3044\u308b\u3068\u8a00\u308f\u308c\u307e\u3059\u3002<\/p><ul><li>\u30a4\u30d9\u30f3\u30c8<i>B<\/i>\u304c\u767a\u751f\u3057\u305f\u3053\u3068\u304c\u308f\u304b\u3063\u3066\u3044\u308b\u5834\u5408 (\u4e88\u5f8c<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ \\mathbb{P}(A\\mid B)\\ } $$<\/div> \uff09\u3001<\/li><li>\u30a4\u30d9\u30f3\u30c8<i>B<\/i>\u304c\u767a\u751f\u3057\u306a\u304b\u3063\u305f\u3053\u3068\u304c\u308f\u304b\u3063\u3066\u3044\u308b\u5834\u5408 (\u4e88\u5f8c<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ \\mathbb{P}(A\\mid \\overline{B})\\ } $$<\/div> \uff09\u3001<\/li><li>\u30a4\u30d9\u30f3\u30c8<i>B<\/i>\u306e\u72b6\u614b (\u4e88\u5f8c) \u306b\u3064\u3044\u3066\u4f55\u3082\u77e5\u3089\u306a\u3044\u5834\u5408<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ \\mathbb{P}(A)\\ } $$<\/div> \uff09\u3002<\/li><\/ul><p>\u8a00\u3044\u63db\u3048\u308c\u3070\u3001\u4e8b\u8c61<i>A<\/i>\u306b\u95a2\u3059\u308b\u79c1\u305f\u3061\u306e\u4e88\u5f8c\u304c<i>B<\/i>\u306b\u95a2\u3059\u308b\u3044\u304b\u306a\u308b\u60c5\u5831\u306b\u3082\u5f71\u97ff\u3055\u308c\u305a\u3001\u307e\u305f<i>B<\/i>\u306b\u95a2\u3059\u308b\u60c5\u5831\u306e\u6b20\u5982\u306b\u3088\u3063\u3066\u3082\u5f71\u97ff\u3055\u308c\u306a\u3044\u5834\u5408\u3001 <i>A<\/i>\u306f<i>B<\/i>\u304b\u3089\u72ec\u7acb\u3057\u3066\u3044\u308b\u3068\u8a00\u308f\u308c\u307e\u3059\u3002\u6761\u4ef6\u4ed8\u304d\u78ba\u7387\u3092\u4f7f\u7528\u3057\u3066\u3001\u5b9a\u7fa9\u306b\u304a\u3051\u308b<i>A<\/i>\u3068<i>B<\/i>\u306e\u5f79\u5272\u3092\u4ea4\u63db\u3067\u304d\u307e\u3059\u3002\u305f\u3060\u3057\u3001\u3082\u3061\u308d\u3093\u3001 <i>A<\/i>\u304c<i>\u4e0d\u53ef\u80fd<\/i>\u3067\u3042\u308a\u3001 <i>A<\/i>\u304c<i>\u78ba\u5b9f<\/i>\u3067\u3042\u308b\u3068\u3044\u3046\u8208\u5473\u306e\u306a\u3044\u7279\u5b9a\u306e\u30b1\u30fc\u30b9\u3092\u9664\u5916\u3057\u307e\u3059\u3002<\/p><p>\u6761\u4ef6\u4ed8\u304d\u78ba\u7387\u3092\u4f7f\u7528\u3057\u305f\u5b9a\u7fa9\u306f\u3088\u308a\u76f4\u89b3\u7684\u3067\u3059\u304c\u3001\u4e00\u822c\u6027\u304c\u4f4e\u304f\u30012 \u3064\u306e\u30a4\u30d9\u30f3\u30c8<i>A<\/i>\u3068<i>B \u304c<\/i>\u5bfe\u79f0\u7684\u306a\u5f79\u5272\u3092\u679c\u305f\u3055\u306a\u3044\u3068\u3044\u3046\u6b20\u70b9\u304c\u3042\u308a\u307e\u3059\u3002<\/p><p>\u307e\u305f\u3001\u7279\u5b9a\u306e\u30a4\u30d9\u30f3\u30c8<i>A \u306f\u3001<\/i>\u305d\u308c\u304c<span><a href=\"https:\/\/science-hub.click\/?p=95765\">\u3069\u306e\u3088\u3046\u306a<\/a><\/span>\u30a4\u30d9\u30f3\u30c8<i>B<\/i>\u3067\u3042\u3063\u3066\u3082\u72ec\u7acb\u3057\u3066\u3044\u308b\u3053\u3068\u306b\u3082\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u4e0d\u53ef\u80fd\u306a\u51fa\u6765\u4e8b\u306f\u3001\u4ed6\u306e\u51fa\u6765\u4e8b\u304b\u3089\u3082\u72ec\u7acb\u3057\u3066\u3044\u307e\u3059\u3002\u7279\u306b\u3001\u30a4\u30d9\u30f3\u30c8<i>A<\/i>\u306f\u3001 <i>A<\/i>\u304c\u78ba\u5b9f\u3067\u3042\u308b\u304b\u4e0d\u53ef\u80fd\u3067\u3042\u308b\u3068\u3044\u3046\u6761\u4ef6\u3067\u3001\u305d\u308c\u81ea\u4f53\u304b\u3089\u72ec\u7acb\u3057\u3066\u3044\u307e\u3059\u3002\u5b9f\u969b\u3001\u30a4\u30d9\u30f3\u30c8<i>A<\/i>\u304c\u305d\u308c\u81ea\u4f53\u304b\u3089\u72ec\u7acb\u3057\u3066\u3044\u308b\u5834\u5408\u3001\u6b21\u306e\u3088\u3046\u306b\u66f8\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 <\/p><center><div class=\"math-formual notranslate\">$$ {\\mathbb{P}(A) = \\mathbb{P}(A \\cap A) = \\mathbb{P}(A)\\mathbb{P}(A),\\,} $$<\/div><\/center><p>\u305d\u3057\u3066\u3001\u30a4\u30d9\u30f3\u30c8<i>A<\/i>\u306e\u78ba\u7387\u306f 0 \u307e\u305f\u306f 1 \u3067\u3042\u308b\u3068\u63a8\u6e2c\u3057\u307e\u3059\u3002<\/p><h2>\u78ba\u7387\u5909\u6570\u306e\u72ec\u7acb\u6027<\/h2><figure class=\"wp-block-image size-large is-style-default\">\n<img decoding=\"async\" alt=\"\u72ec\u7acb\u6027 (\u78ba\u7387)\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\" class=\"aligncenter\" onerror=\"this.style.display=none;\" src=\"https:\/\/img.youtube.com\/vi\/tNAqLwDYpW8\/0.jpg\" style=\"width:100%;\"\/><\/figure><h3><span>\u5b9a\u7fa9<\/span><\/h3><p>\u78ba\u7387\u5909\u6570\u306e<span><a href=\"https:\/\/science-hub.click\/?p=13526\">\u6709\u9650\u65cf<\/a><\/span>\u306e\u72ec\u7acb\u6027\u306b\u3064\u3044\u3066\u306f\u3001\u540c\u7b49\u306e\u5b9a\u7fa9\u304c\u3044\u304f\u3064\u304b\u3042\u308a\u307e\u3059\u3002\u7279\u306b\u90e8\u65cf\u306e\u5bb6\u65cf\u306e\u72ec\u7acb\u6027\u3092\u5b9a\u7fa9\u3057\u3001\u30a4\u30d9\u30f3\u30c8\u306e\u72ec\u7acb\u6027\u3068\u78ba\u7387\u5909\u6570\u306e\u72ec\u7acb\u6027\u3092\u90e8\u65cf\u306e\u72ec\u7acb\u6027\u306e\u7279\u6b8a\u306a\u30b1\u30fc\u30b9\u3068\u3057\u3066\u898b\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u90e8\u65cf\u306b\u3064\u3044\u3066\u3001\u72ec\u7acb\u6027\u306b\u95a2\u3059\u308b\u7279\u5b9a\u306e\u4e00\u822c\u7684\u306a\u7d50\u679c\u3092 1 \u56de\u3060\u3051\u5b9f\u8a3c\u3057\u3001\u3053\u306e\u4e00\u822c\u7684\u306a\u7d50\u679c\u306e\u300c\u30a4\u30d9\u30f3\u30c8\u300d\u30d0\u30fc\u30b8\u30e7\u30f3\u3068\u300c\u78ba\u7387\u5909\u6570\u300d\u30d0\u30fc\u30b8\u30e7\u30f3\u3092\u5373\u5ea7\u306b\u63a8\u5b9a\u3059\u308b\u3053\u3068\u304c\u53ef\u80fd\u306b\u306a\u308a\u307e\u3059 (\u30b0\u30eb\u30fc\u30d7\u5316\u88dc\u984c\u304c\u305d\u306e\u4f8b\u3067\u3059)\u3002\u305f\u3060\u3057\u3001\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u306b\u6709\u52b9\u306a\u78ba\u7387\u5909\u6570\u306e\u72ec\u7acb\u6027\u306b\u95a2\u3059\u308b 2 \u3064\u306e\u5b9a\u7fa9\u3068\u3044\u304f\u3064\u304b\u306e\u4fbf\u5229\u306a\u57fa\u6e96\u3092\u6700\u521d\u306b\u4e0e\u3048\u308b\u3053\u3068\u304c\u304a\u305d\u3089\u304f\u597d\u307e\u3057\u3044\u3067\u3057\u3087\u3046\u3002\u4ee5\u4e0b\u3067\u306f\u3001\u30b7\u30fc\u30b1\u30f3\u30b9\u3092\u691c\u8a0e\u3057\u307e\u3059<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ (X_1, X_2, \\dots,X_n)} $$<\/div>\u540c\u3058\u78ba\u7387\u7a7a\u9593\u4e0a\u3067\u5b9a\u7fa9\u3055\u308c\u305f\u78ba\u7387\u5909\u6570\u306e\u6570<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ (\\Omega, \\mathcal{A}, \\mathbb{P})} $$<\/div> \u3001\u305f\u3060\u3057\u3001\u7570\u306a\u308b\u7a7a\u9593\u306e\u5024\u3092\u6301\u3064\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059: <div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ X_i\\\u00a0:\\ (\\Omega, \\mathcal{A}, \\mathbb{P})\\ \\rightarrow\\ (E_i,\\mathcal{E}_i),\\quad 1\\le i\\le n.} $$<\/div><\/p><div><p><strong>\u610f\u5473<\/strong><span>&#8211;<\/span> <div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ (X_1, X_2, \\dots,X_n)} $$<\/div>\u6b21\u306e 2 \u3064\u306e\u6761\u4ef6\u306e\u3044\u305a\u308c\u304b\u304c\u6e80\u305f\u3055\u308c\u308b\u5834\u5408\u3001 \u306f\u72ec\u7acb\u78ba\u7387\u5909\u6570\u306e\u30d5\u30a1\u30df\u30ea\u30fc\u306b\u306a\u308a\u307e\u3059\u3002 <\/p><ul><li><div class=\"math-formual notranslate\">$$ {\\forall (A_1,\\dots,A_n)\\in\\mathcal{E}_1\\times\\dots\\times\\mathcal{E}_n,\\quad\\mathbb{P}(X_1\\in A_1\\text{ et }X_2\\in A_2\\text{ et }\\dots\\text{ et }X_n\\in A_n)\\ =\\  \\prod_{i=1}^n\\mathbb{P}(X_i\\in A_i),} $$<\/div><\/li><li>\u79c1\u305f\u3061\u306b\u306f\u5e73\u7b49\u304c\u3042\u308b<\/li><\/ul><dl><dd><div class=\"math-formual notranslate\">$$ {\\mathbb{E}\\left[\\prod_{i=1}^n\\ \\varphi_i(X_i)\\right]\\ =\\  \\prod_{i=1}^n\\mathbb{E}\\left[\\varphi_i(X_i)\\right],} $$<\/div><\/dd><\/dl><dl><dd>\u3042\u3089\u3086\u308b\u95a2\u6570\u30b9\u30a4\u30fc\u30c8\u306b\u5bfe\u5fdc<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ \\phi_i} $$<\/div>\u306b\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u307e\u3059<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ (E_i,\\mathcal{E}_i),} $$<\/div>\u306e\u5024\u3092\u6301\u3064<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ \\R,\\ } $$<\/div>\u4e0a\u8a18\u306e\u671f\u5f85\u304c\u610f\u5473\u3092\u306a\u3059\u3088\u3046\u306b\u306a\u308b\u3068\u3059\u3050\u306b\u3002<\/dd><\/dl><\/div><p>\u4e0a\u8a18\u306e\u671f\u5f85\u306f\u3001\u6b21\u306e\u5834\u5408\u306b\u610f\u5473\u3092\u6210\u3057\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ \\varphi_i\\ } $$<\/div>\u6e2c\u5b9a\u53ef\u80fd\u3067\u3042\u308a\u3001\u3082\u3057<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ \\prod_{i=1}^n\\ \\varphi_i(X_i)\\ } $$<\/div>\u7a4d\u5206\u53ef\u80fd\u3067\u3042\u308b\u304b\u3001\u307e\u305f\u306f<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ \\varphi_i\\ } $$<\/div>\u306f\u6b63\u307e\u305f\u306f\u30bc\u30ed\u3067\u3059\u3002\u901a\u5e38\u3001\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u3067\u306f\u3001 <div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ (E_i,\\mathcal{E}_i)=(\\mathbb{R}^{d_i},\\mathcal{B}(\\mathbb{R}^{d_i})).} $$<\/div> 2 \u3064\u306e\u5b9f\u969b\u306e\u78ba\u7387\u5909\u6570\u306e\u5834\u5408\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p><div><p><strong>\u5b9a\u7fa9<\/strong><span>\u2014<\/span>\u6b21\u306e 2 \u3064\u306e\u6761\u4ef6\u306e\u3044\u305a\u308c\u304b\u304c\u6e80\u305f\u3055\u308c\u308b\u5834\u5408\u30012 \u3064\u306e\u5b9f\u6570\u78ba\u7387\u5909\u6570<i>X<\/i>\u3068<i>Y<\/i>\u306f\u72ec\u7acb\u3057\u3066\u3044\u307e\u3059\u3002 <\/p><ul><li><div class=\"math-formual notranslate\">$$ {\\forall (A,B)\\in\\mathcal{B}(\\mathbb{R})^{2},\\quad\\mathbb{P}(X\\in A\\text{ et }Y\\in B)\\ =\\  \\mathbb{P}(X\\in A)\\ \\mathbb{P}(Y\\in B),} $$<\/div><\/li><li>\u6211\u3005\u306f\u6301\u3063\u3066\u3044\u307e\u3059<\/li><\/ul><dl><dd><div class=\"math-formual notranslate\">$$ {\\mathbb{E}\\left[g(X)\\cdot h(Y)\\right] = \\mathbb{E}[g(X)]\\cdot \\mathbb{E}[h(Y)]} $$<\/div><\/dd><\/dl><dl><dd>\u30dc\u30ec\u30ea\u30a2\u30f3\u95a2\u6570\u306e\u4efb\u610f\u306e\u30da\u30a2\u306b\u5bfe\u3057\u3066<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ g} $$<\/div>\u305d\u3057\u3066<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ h,\\ } $$<\/div>\u4e0a\u8a18\u306e\u671f\u5f85\u304c\u610f\u5473\u3092\u306a\u3059\u3088\u3046\u306b\u306a\u308b\u3068\u3059\u3050\u306b\u3002<\/dd><\/dl><\/div><p>\u524d\u8ff0\u306e\u5b9a\u7fa9\u306f\u3001\u4fbf\u5b9c\u4e0a 1 \u304b\u3089<i>n<\/i>\u307e\u3067\u756a\u53f7\u3092\u4ed8\u3051\u305f\u78ba\u7387\u5909\u6570\u306e<i><b>\u6709\u9650<\/b><\/i>\u65cf\u3092\u6271\u3044\u307e\u3059\u304c\u3001\u3053\u308c\u306b\u3088\u3063\u3066\u30b9\u30c6\u30fc\u30c8\u30e1\u30f3\u30c8\u306e\u4e00\u822c\u6027\u304c\u5236\u9650\u3055\u308c\u308b\u3053\u3068\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u5b9f\u969b\u3001\u78ba\u7387\u5909\u6570\u306e\u6709\u9650\u65cf\u306e\u8981\u7d20\u306b\u306f\u5e38\u306b 1 \u304b\u3089<i>n<\/i>\u307e\u3067\u306e\u756a\u53f7\u3092\u4ed8\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u5b9a\u7fa9\u3067\u306f\u30d5\u30a1\u30df\u30ea\u30fc\u306e\u5404\u8981\u7d20\u304c\u5bfe\u79f0\u7684\u306a\u5f79\u5272\u3092\u679c\u305f\u3059\u305f\u3081\u3001\u3069\u3061\u3089\u306e\u756a\u53f7\u3092\u9078\u629e\u3057\u3066\u3082\u5b9a\u7fa9\u306e\u691c\u8a3c\u306b\u306f\u5f71\u97ff\u3057\u307e\u305b\u3093\u3002<\/p><p>\u4efb\u610f\u306e (\u304a\u305d\u3089\u304f\u7121\u9650\u306e) \u78ba\u7387\u5909\u6570\u65cf\u306e\u72ec\u7acb\u6027\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002<\/p><div><p><strong>\u5b9a\u7fa9<\/strong><span>&#8211;<\/span><b>\u4efb\u610f\u306e<\/b>\u5bb6\u65cf<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ (X_{j})_{j\\in J}\\ } $$<\/div>\u306b\u5b9a\u7fa9\u3055\u308c\u305f\u78ba\u7387\u5909\u6570\u306e\u6570<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ (\\Omega,\\mathcal{A},\\mathbb{P})\\ } $$<\/div>\u306e<i>\u6709\u9650\u30b5\u30d6\u30d5\u30a1\u30df\u30ea\u30fc<\/i>\u304c\u5b58\u5728\u3059\u308b\u5834\u5408\u306b\u9650\u308a\u3001<i>\u72ec\u7acb<\/i>\u78ba\u7387\u5909\u6570\u306e\u30d5\u30a1\u30df\u30ea\u30fc\u3068\u306a\u308a\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ (X_{j})_{j\\in J}\\ } $$<\/div>\u306f\u72ec\u7acb\u3057\u305f\u78ba\u7387\u5909\u6570\u306e\u65cf\u3067\u3059 (\u3064\u307e\u308a\u3001 <i>J<\/i>\u306e\u4efb\u610f\u306e\u6709\u9650\u90e8\u5206<i>I<\/i>\u306b\u5bfe\u3057\u3066\u3001\u6b21\u306e\u5834\u5408\u306b\u9650\u308a\u3001 <div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ (X_{i})_{i\\in I}\\ } $$<\/div>\u306f\u72ec\u7acb\u3057\u305f\u78ba\u7387\u5909\u6570\u306e\u30d5\u30a1\u30df\u30ea\u30fc\u3067\u3059)\u3002<\/p><\/div><h3><span><span><a href=\"https:\/\/science-hub.click\/?p=37332\">\u5bc6\u5ea6<\/a><\/span>\u306e\u3042\u308b\u78ba\u7387\u5909\u6570\u306e\u5834\u5408<\/span><\/h3><p>\u305d\u308c\u3068\u3082\u7d9a\u7de8\u304b<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ X=(X_1, X_2, \\dots,X_n)} $$<\/div>\u540c\u3058\u78ba\u7387\u7a7a\u9593\u4e0a\u3067\u5b9a\u7fa9\u3055\u308c\u305f\u5b9f\u969b\u306e\u78ba\u7387\u5909\u6570\u306e\u6570<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ (\\Omega, \\mathcal{A}, \\mathbb{P}).\\ } $$<\/div><\/p><div><p><strong><span>\u5b9a\u7406<\/span><\/strong><span>\u2014<\/span><\/p><ul><li>\u3082\u3057<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ X\\ } $$<\/div>\u78ba\u7387\u5bc6\u5ea6\u304c\u3042\u308b<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ f:\\R^n\\rightarrow [0,+\\infty[\\ } $$<\/div>\u3053\u308c\u306f\u300c\u88fd\u54c1\u300d\u5f62\u5f0f\u3067\u66f8\u304b\u308c\u3066\u3044\u307e\u3059\u3002 <\/li><\/ul><dl><dd><div class=\"math-formual notranslate\">$$ {\\forall x=(x_1,\\dots,x_n)\\in\\R^n,\\qquad f(x)\\ =\\  \\prod_{i=1}^ng_i(x_i),} $$<\/div><\/dd><\/dl><dl><dd>\u95a2\u6570\u306f\u3069\u3053\u306b\u3042\u308b\u306e\u304b<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ g_i\\ } $$<\/div>\u30dc\u30ec\u30ea\u30a2\u30f3\u3067\u6b63\u307e\u305f\u306f\u30bc\u30ed\u306e\u5834\u5408\u3001 <div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ X\\ } $$<\/div>\u306f\u4e00\u9023\u306e\u72ec\u7acb\u5909\u6570\u3067\u3059\u3002\u3055\u3089\u306b\u3001\u6a5f\u80fd<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ f_i\\ } $$<\/div>\u306b\u3088\u3063\u3066\u5b9a\u7fa9\u3055\u308c\u308b<\/dd><\/dl><dl><dd><div class=\"math-formual notranslate\">$$ {f_i(x)\\ =\\  \\frac{g_i(x)}{\\int_{\\R}g_i(u)du}} $$<\/div><\/dd><\/dl><dl><dd>\u306f<span><a href=\"https:\/\/science-hub.click\/?p=20826\">\u78ba\u7387\u5909\u6570<\/a><\/span>\u306e\u78ba\u7387\u5bc6\u5ea6\u3067\u3059<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ X_i.\\ } $$<\/div><\/dd><\/dl><ul><li>\u9006\u306b\u3001\u3082\u3057<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ X\\ } $$<\/div>\u305d\u308c\u305e\u308c\u306e\u78ba\u7387\u5bc6\u5ea6\u306e\u72ec\u7acb\u3057\u305f\u5b9f\u78ba\u7387\u5909\u6570\u306e\u30b7\u30fc\u30b1\u30f3\u30b9\u3067\u3059<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ f_i,\\ } $$<\/div>\u305d\u308c\u3067<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ X\\ } $$<\/div>\u306f\u78ba\u7387\u5bc6\u5ea6\u3092\u6301\u3061\u3001\u95a2\u6570\u306f<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ f\\ } $$<\/div>\u306b\u3088\u3063\u3066\u5b9a\u7fa9\u3055\u308c\u308b<\/li><\/ul><dl><dd><div class=\"math-formual notranslate\">$$ {\\forall (x_1,\\dots,x_n)\\in\\R^n,\\qquad f(x_1,\\dots,x_n)\\ =\\  \\prod_{i=1}^nf_i(x_i),} $$<\/div><\/dd><dd>\u306f\u78ba\u7387\u5bc6\u5ea6\u3067\u3059<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ X.\\ } $$<\/div><\/dd><\/dl><\/div><div><div><p><b>\u76f4\u63a5\u7684\u306a\u610f\u5473\u3002<\/b><\/p><p>\u5bc6\u5ea6\u306e\u3088\u3046\u306a\u3082\u306e<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ f\\ } $$<\/div>\u88fd\u54c1\u306e\u5f62\u3067\u3001\u79c1\u305f\u3061\u306f\u6301\u3063\u3066\u3044\u307e\u3059<\/p><center><div class=\"math-formual notranslate\">$$ {\\begin{align} 1 &amp;= \\int_{\\R^2}f(x_1,x_2) \\, dx_1 \\, dx_2\\\\ &amp;=\\left(\\int g_1(x_1)\\, dx_1\\right) \\, \\left(\\int g_2(x_2) \\, dx_2\\right) \\end{align} } $$<\/div><\/center><p>\u305d\u3057\u3066\u305d\u306e\u5f8c<\/p><center><div class=\"math-formual notranslate\">$$ {\\begin{align} f(x_1,x_2)  &amp;= g_1(x_1)\\, g_2(x_2) \\\\ &amp;= \\frac{g_1(x_{1})}{\\int_{\\R}g_1(u)du}\\ \\frac{g_2(x_{2})}{\\int_{\\R}g_2(v)dv}\\\\ &amp;= f_1(x_1) \\,f_{2}(x_2). \\end{align}} $$<\/div><\/center><p>\u69cb\u9020\u306b\u3088\u308b\u6a5f\u80fd<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ f_i\\ } $$<\/div>\u306f\u6574\u6570 1 \u306a\u306e\u3067\u3001 <\/p><center><div class=\"math-formual notranslate\">$$ {\\begin{align} \\int_{\\R} f(x_1,x_2) dx_2  &amp;= f_1(x_1), \\\\ \\int_{\\R} f(x_1,x_2) dx_1  &amp;= f_2(x_2). \\end{align}} $$<\/div><\/center><p>\u3057\u305f\u304c\u3063\u3066\u3001\u95a2\u6570\u306f<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ f_i\\ } $$<\/div>\u306f\u3001\u6b21\u306e 2 \u3064\u306e\u6210\u5206\u306e\u5468\u8fba\u78ba\u7387\u5bc6\u5ea6\u3067\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ X.\\ } $$<\/div>\u3057\u305f\u304c\u3063\u3066\u3001\u95a2\u6570\u306e\u4efb\u610f\u306e\u30da\u30a2\u306b\u5bfe\u3057\u3066\u3001 <div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ \\varphi\\ } $$<\/div>\u305d\u3057\u3066<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ \\psi\\ } $$<\/div>\u4ee5\u4e0b\u306e\u6700\u521d\u306e\u9805\u304c\u610f\u5473\u3092\u6301\u3064\u3088\u3046\u306b\u3001 <\/p><center><div class=\"math-formual notranslate\">$$ {\\begin{align} \\operatorname{E}[\\varphi(X_1)\\psi(X_2)] &amp;= \\int \\int \\varphi(x_1)\\psi(x_2)f(x_1,x_2) \\, dx_1 \\, dx_2\\\\ &amp;= \\int \\int \\varphi(x_1)f_1(x_1)\\psi(x_2)f_2(x_2) \\, dx_1 \\, dx_2\\\\ &amp;= \\int \\varphi(x_1)f_1(x_1) \\, dx_1 \\int \\psi(x_2)f_{2}(x_2) \\, dx_2\\\\ &amp;= \\operatorname{E}[\\varphi(X_1)] \\operatorname{E}[\\psi(X_2)]\\end{align}} $$<\/div><\/center><p>\u3053\u308c\u306f\u5909\u6570\u306e\u72ec\u7acb\u6027\u306b\u3064\u306a\u304c\u308a\u307e\u3059<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ X_{1}\\ } $$<\/div>\u305d\u3057\u3066<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ X_{2}.\\ } $$<\/div><\/p><p><b>\u76f8\u4e92\u7684\u306a\u610f\u5473\u3002<\/b>\u305d\u308c\u3092\u793a\u3059\u3060\u3051\u3067\u5341\u5206\u3067\u3059<\/p><center><div class=\"math-formual notranslate\">$$ {\\forall A\\in \\mathcal{B}(\\R^2),\\quad \\mathbb{P}_{X}(A)=\\mu(A),} $$<\/div><\/center><p>\u307e\u305f\u306f<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ \\mathbb{P}_{X}\\ } $$<\/div>\u306e\u6cd5\u5247\u3067\u3059<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ X,\\ } $$<\/div>\u305d\u3057\u3066\u3069\u3053\u3067<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ \\mu\\ } $$<\/div>\u5bc6\u5ea6\u3092\u6301\u3064\u30e1\u30b8\u30e3\u30fc\u3067\u3059<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\  (x_1,x_2)\\rightarrow f_1(x_1)f_{2}(x_2).\\ } $$<\/div>\u91d1<\/p><center><div class=\"math-formual notranslate\">$$ {\\forall A\\in \\mathcal{C},\\quad \\mathbb{P}_{X}(A)=\\mu(A),} $$<\/div><\/center><p>\u307e\u305f\u306f<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ \\mathcal{C}\\ } $$<\/div>\u30dc\u30ec\u30ea\u30a2\u30f3 \u30bf\u30a4\u30eb\u306e\u30af\u30e9\u30b9\u3067\u3059\u3002 <\/p><center><div class=\"math-formual notranslate\">$$ {\\mathcal{C}\\ =\\ \\{A_1\\times A_2\\ |\\ A_i\\in\\mathcal{B}(\\R),i\\in\\{1,2\\}\\}. } $$<\/div><\/center><p>\u78ba\u304b\u306b<\/p><center><div class=\"math-formual notranslate\">$$ {\\begin{align} \\mathbb{P}_{X}(A_1\\times A_2) &amp;= \\mathbb{P}(X_1\\in A_1\\text{ et }X_2\\in A_2)\\\\ &amp;= \\mathbb{P}(X_1\\in A_1)\\mathbb{P}(X_2\\in A_2)\\\\ &amp;= \\left(\\int_{\\R} 1_{A_1}(x_1)f_1(x_1) \\, dx_1\\right)\\left(\\int_{\\R} 1_{A_2}(x_2)f_2(x_2) \\, dx_2\\right)\\\\ &amp;= \\int_{\\R^2} 1_{A_1\\times A_2}(x_1,x_2)f_1(x_1)f_2(x_2) \\, dx_1 \\, dx_2\\\\ &amp;= \\mu(A_1\\times A_2)\\end{align}.} $$<\/div><\/center><p>\u305d\u306e\u3068\u304d\u79c1\u305f\u3061\u306f\u305d\u308c\u306b\u6c17\u3065\u304d\u307e\u3059<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ \\mathcal{C}\\ } $$<\/div>\u306f \u03c0 \u30b7\u30b9\u30c6\u30e0\u3067\u3042\u308a\u3001\u306b\u3088\u3063\u3066\u751f\u6210\u3055\u308c\u308b\u90e8\u65cf\u3067\u3042\u308b\u3068\u8003\u3048\u3089\u308c\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ \\mathcal{C}\\ } $$<\/div>\u6771<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\  \\mathcal{B}(\\R^2),\\ } $$<\/div>\u3057\u305f\u304c\u3063\u3066\u3001\u78ba\u7387\u6e2c\u5ea6\u306e\u4e00\u610f\u6027\u306e\u88dc\u984c\u306b\u3088\u308a\u3001 <\/p><center><div class=\"math-formual notranslate\">$$ {\\forall A\\in \\mathcal{B}(\\R^2),\\quad \\mathbb{P}_{X}(A)=\\mu(A).} $$<\/div><\/center><\/div><\/div><h3><span>\u96e2\u6563\u5909\u6570\u306e\u5834\u5408<\/span><\/h3><p>\u96e2\u6563\u5909\u6570\u306e\u5834\u5408\u3001\u6709\u7528\u306a\u72ec\u7acb\u6027\u57fa\u6e96\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002<\/p><div><p><strong>\u96e2\u6563\u306e\u5834\u5408<\/strong><span>\u2014<\/span> <i>X=(X <sub>1<\/sub> , X <sub>2<\/sub> , &#8230;, X <sub>n<\/sub> )<\/i>\u3092\u96e2\u6563\u78ba\u7387\u5909\u6570\u306e\u30b7\u30fc\u30b1\u30f3\u30b9\u3068\u3057\u3001 <i>(S <sub>1<\/sub> , S <sub>2<\/sub> , &#8230;, S <sub>n<\/sub> )<\/i>\u3092\u6709\u9650\u96c6\u5408\u306e\u30b7\u30fc\u30b1\u30f3\u30b9\u3068\u3059\u308b\u307e\u305f\u306f\u3001\u3059\u3079\u3066\u306e<i>i\u2264n<\/i>\u306b\u3064\u3044\u3066\u3001\u53ef\u7b97\u3067\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ \\mathbb{P}(X_i\\in S_i)=1.\\ } $$<\/div>\u3053\u306e\u5834\u5408\u3001\u30d5\u30a1\u30df\u30ea\u30fc<i>(X <sub>1<\/sub> , X <sub>2<\/sub> , &#8230; , X <sub>n<\/sub> )<\/i>\u306f\u3001\u3059\u3079\u3066\u306e\u5834\u5408\u3001\u72ec\u7acb\u3057\u305f\u78ba\u7387\u5909\u6570\u306e\u30b7\u30fc\u30b1\u30f3\u30b9\u306b\u306a\u308a\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ x=(x_1,x_2, \\dots, x_n)\\in \\prod_{i=1}^n\\,S_i,\\ } $$<\/div><\/p><center><div class=\"math-formual notranslate\">$$ { \\mathbb{P}\\left(X= x\\right)\\ =\\ \\prod_{i=1}^n\\,\\mathbb{P}\\left(X_i= x_i\\right).} $$<\/div><\/center><\/div><div> <strong><span><a href=\"https:\/\/science-hub.click\/?p=33222\">\u30c7\u30ab\u30eb\u30c8\u7a4d<\/a><\/span>\u306b\u95a2\u3059\u308b\u7d71\u4e00\u6cd5\u5247:<\/strong><div><ul><li> <i>(E <sub>1<\/sub> , E <sub>2<\/sub> , &#8230; , E <sub>n<\/sub> ) \u3092<\/i>\u305d\u308c\u305e\u308c\u306e\u57fa\u6570<i>#E <sub>i<\/sub><\/i>\u306e\u6709\u9650\u96c6\u5408\u306e\u30b7\u30fc\u30b1\u30f3\u30b9\u3068\u3057\u3001 <i>X=(X <sub>1<\/sub> , X <sub>2<\/sub> , &#8230; , X <sub>n<\/sub> )<\/i>\u3092\u30e9\u30f3\u30c0\u30e0\u3068\u3057\u307e\u3059\u3002\u30c7\u30ab\u30eb\u30c8\u7a4d\u306e\u5024\u3092\u6301\u3064<span><a href=\"https:\/\/science-hub.click\/?p=72623\">\u5909\u6570<\/a><\/span>uniform\uff1a <\/li><\/ul><center><div class=\"math-formual notranslate\">$$ { E\\ =\\ E_1\\times E_2\\times E_3\\times\\ \\dots\\ \\times E_n.} $$<\/div><\/center><dl><dd>\u3053\u306e\u5834\u5408\u3001\u30b7\u30fc\u30b1\u30f3\u30b9<i>X \u306f<\/i>\u72ec\u7acb\u3057\u305f\u78ba\u7387\u5909\u6570\u306e\u30b7\u30fc\u30b1\u30f3\u30b9\u3067\u3042\u308a\u3001\u5404<i>i<\/i>\u306b\u3064\u3044\u3066\u3001\u78ba\u7387\u5909\u6570<i>X <sub>i \u306f<\/sub><\/i><i>E <sub>i<\/sub><\/i>\u306b\u95a2\u3059\u308b\u4e00\u69d8\u6cd5\u5247\u306b\u5f93\u3044\u307e\u3059\u3002\u5b9f\u969b\u306b\u3001\u5404<i>Y <sub>i \u304c<\/sub><\/i>\u5bfe\u5fdc\u3059\u308b<span><a href=\"https:\/\/science-hub.click\/?p=57227\">\u30bb\u30c3\u30c8<\/a><\/span><i>E <sub>i<\/sub><\/i>\u306b\u308f\u305f\u3063\u3066\u5747\u4e00\u3067\u3042\u308b\u3001\u72ec\u7acb\u78ba\u7387\u5909\u6570\u306e\u30b7\u30fc\u30b1\u30f3\u30b9<i>Y=(Y <sub>i<\/sub> ) <sub>1\u2264i\u2264n<\/sub><\/i>\u3092\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u6b21\u306b\u3001 <i>E<\/i>\u306e\u4efb\u610f\u306e\u8981\u7d20<i>x=(x <sub>1<\/sub> , x <sub>2<\/sub> , &#8230;, x <sub>n<\/sub> )<\/i>\u306b\u3064\u3044\u3066\u3001 <\/dd><\/dl><center><div class=\"math-formual notranslate\">$$ { \\begin{align}\\mathbb{P}\\left(X= x\\right)&amp;=\\frac1{\\# E}\\\\ &amp;=\\prod_{i=1}^n\\frac1{\\# E_i}\\\\ &amp;=\\prod_{i=1}^n\\,\\mathbb{P}\\left(Y_i= x_i\\right)\\\\ &amp;= \\mathbb{P}\\left(Y= x\\right),\\end{align}} $$<\/div><\/center><dl><dd> 2 \u756a\u76ee\u306e\u7b49\u5f0f\u306f\u96c6\u5408\u306e\u30c7\u30ab\u30eb\u30c8\u7a4d\u306e\u8981\u7d20\u306e<span><a href=\"https:\/\/science-hub.click\/?p=71097\">\u6570\u3092<\/a><\/span>\u4e0e\u3048\u308b\u516c\u5f0f\u304b\u3089<span><a href=\"https:\/\/science-hub.click\/?p=61597\">\u5f97\u3089\u308c<\/a><\/span>\u30014 \u756a\u76ee\u306f<i>Y <sub>i<\/sub><\/i>\u306e\u72ec\u7acb\u6027\u304b\u3089\u5f97\u3089\u308c\u3001\u4ed6\u306e\u7b49\u5f0f\u306f\u4e00\u69d8\u6cd5\u5247\u306e\u5b9a\u7fa9\u304b\u3089\u5f97\u3089\u308c\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u30b7\u30fc\u30b1\u30f3\u30b9<i>X<\/i>\u3068<i>Y \u306f<\/i>\u540c\u3058\u6cd5\u5247\u3092\u6301\u3061\u307e\u3059\u3002\u3053\u308c\u306f\u3001 <i>X<\/i>\u304c\u4e00\u9023\u306e\u72ec\u7acb\u3057\u305f\u78ba\u7387\u5909\u6570\u3067\u3042\u308a\u3001\u305d\u306e\u6210\u5206\u304c\u5747\u4e00\u306e\u6cd5\u5247\u306b\u5f93\u3046\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002<\/dd><\/dl><ul><li>\u3053\u306e\u57fa\u6e96\u306e\u9069\u7528\u306f\u3001<span><a href=\"https:\/\/science-hub.click\/?p=49311\">\u9806\u5217<\/a><\/span>\u306e<span><a href=\"https:\/\/science-hub.click\/?p=73733\">\u30ec\u30fc\u30de\u30fc \u30b3\u30fc\u30c9<\/a><\/span>\u306e\u30b3\u30f3\u30dd\u30fc\u30cd\u30f3\u30c8\u306e\u72ec\u7acb\u6027\u3067\u3042\u308a\u3001\u3053\u308c\u306b\u3088\u308a\u3001\u7b2c 1<span><a href=\"https:\/\/science-hub.click\/?p=93809\">\u7a2e<\/a><\/span>\u30b9\u30bf\u30fc\u30ea\u30f3\u30b0\u6570\u306e<span><a href=\"https:\/\/science-hub.click\/?p=95231\">\u6bcd\u95a2\u6570\u3092<\/a><\/span>\u7c21\u5358\u306b\u53d6\u5f97\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/li><li>\u5225\u306e\u7528\u9014\u306f\u3001\u533a\u9593 [0,1] \u306b\u304a\u3051\u308b\u5747\u4e00\u306a\u6570\u5024\u306e<span><a href=\"https:\/\/science-hub.click\/?p=39064\">10 \u9032\u6570\u5c55\u958b<\/a><\/span>\u304b\u3089\u306e\u6841\u306e\u72ec\u7acb\u6027\u3067\u3059\u3002<\/li><\/ul><\/div><\/div><figure class=\"wp-block-image size-large is-style-default\">\n<img decoding=\"async\" alt=\"\u72ec\u7acb\u6027 (\u78ba\u7387)\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\" class=\"aligncenter\" onerror=\"this.style.display=none;\" src=\"https:\/\/img.youtube.com\/vi\/REu8ddGgJW8\/0.jpg\" style=\"width:100%;\"\/><\/figure><h3><span>\u305d\u306e\u4ed6\u306e\u72ec\u7acb\u6027\u57fa\u6e96<\/span><\/h3><p>\u4f8b\u3048\u3070\u3001<\/p><div><p><strong>\u57fa\u6e96<\/strong><span>\u2014<\/span> <i>X<\/i>\u3068<i>Y \u3092<\/i><span><a href=\"https:\/\/science-hub.click\/?p=1934\">\u78ba\u7387\u7a7a\u9593<\/a><\/span>\u4e0a\u3067\u5b9a\u7fa9\u3055\u308c\u305f 2 \u3064\u306e\u5b9f\u969b\u306e\u78ba\u7387\u5909\u6570\u3068\u3059\u308b<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ (\\Omega,\\mathcal{A},\\mathbb{P}).\\ } $$<\/div><\/p><ul><li>\u5b9f\u6570\u306e\u4efb\u610f\u306e\u30da\u30a2<i>(x,y)<\/i>\u306b\u3064\u3044\u3066\u3001 <\/li><\/ul><center><div class=\"math-formual notranslate\">$$ { \\mathbb{P}\\left(X\\le x\\text{ et }Y\\le y\\right)\\ =\\ \\mathbb{P}\\left(X\\le x\\right)\\times\\mathbb{P}\\left(Y\\le y\\right),} $$<\/div><\/center><dl><dd>\u305d\u306e\u5834\u5408\u3001 <i>X<\/i>\u3068<i>Y \u306f<\/i>\u72ec\u7acb\u3057\u3066\u3044\u307e\u3059\u3002<\/dd><\/dl><ul><li> <i>Y<\/i>\u306b\u5024\u304c\u3042\u308b\u5834\u5408<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ \\mathbb{N},\\ } $$<\/div>\u305d\u3057\u3066\u3001\u3082\u3057\u3001\u3069\u306e\u30ab\u30c3\u30d7\u30eb\u306b\u3068\u3063\u3066\u3082<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ (x,n)\\in\\mathbb{R}\\times\\mathbb{N},\\ } $$<\/div><\/li><\/ul><center><div class=\"math-formual notranslate\">$$ { \\mathbb{P}\\left(X\\le x\\text{ et }Y=n\\right)\\ =\\ \\mathbb{P}\\left(X\\le x\\right)\\times\\mathbb{P}\\left(Y=n\\right),} $$<\/div><\/center><dl><dd>\u305d\u306e\u5834\u5408\u3001 <i>X<\/i>\u3068<i>Y \u306f<\/i>\u72ec\u7acb\u3057\u3066\u3044\u307e\u3059\u3002<\/dd><\/dl><ul><li>\u3082\u3061\u308d\u3093\u3001 <i>X<\/i>\u3068<i>Y<\/i>\u306b\u5024\u304c\u3042\u308c\u3070\u3001 <div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ \\mathbb{N},\\ } $$<\/div>\u305d\u3057\u3066\u3001\u3082\u3057\u3001\u3069\u306e\u30ab\u30c3\u30d7\u30eb\u306b\u3068\u3063\u3066\u3082<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ (m,n)\\in\\mathbb{N}^2,\\ } $$<\/div><\/li><\/ul><center><div class=\"math-formual notranslate\">$$ { \\mathbb{P}\\left(X=m\\text{ et }Y=n\\right)\\ =\\ \\mathbb{P}\\left(X=m\\right)\\times\\mathbb{P}\\left(Y=n\\right),} $$<\/div><\/center><dl><dd>\u305d\u306e\u5834\u5408\u3001 <i>X<\/i>\u3068<i>Y \u306f<\/i>\u72ec\u7acb\u3057\u3066\u3044\u307e\u3059\u3002<\/dd><\/dl><\/div><p>\u305f\u3068\u3048\u3070\u30012 \u756a\u76ee\u306e\u57fa\u6e96\u3092\u4f7f\u7528\u3057\u3066\u3001\u62d2\u5426\u6cd5\u3067\u306f\u53cd\u5fa9\u56de\u6570\u304c\u53cd\u5fa9\u306e\u6700\u5f8c\u306b\u751f\u6210\u3055\u308c\u308b\u30e9\u30f3\u30c0\u30e0<span>\u30aa\u30d6\u30b8\u30a7\u30af\u30c8<\/span>(\u591a\u304f\u306e\u5834\u5408\u4e71\u6570) \u304b\u3089\u72ec\u7acb\u3057\u3066\u3044\u308b\u3053\u3068\u3092\u5b9f\u8a3c\u3067\u304d\u307e\u3059\u3002<\/p><p>\u3053\u308c\u3089\u306e\u72ec\u7acb\u6027\u57fa\u6e96\u3092\u3001\u5b9f\u969b\u306e\u78ba\u7387\u5909\u6570\u306e<i>\u6709\u9650<\/i>\u65cf\u306b\u4e00\u822c\u5316\u3067\u304d\u307e\u3059\u3002\u305d\u306e\u4e00\u90e8\u306f\u3001\u304a\u305d\u3089\u304f\u3001\u6709\u9650\u307e\u305f\u306f\u53ef\u7b97\u90e8\u5206\u306e\u5024\u3092\u6301\u3064\u96e2\u6563\u5909\u6570\u3067\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ \\mathbb{R},\\ } $$<\/div>\u3068\u306f\u7570\u306a\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ \\mathbb{N}.\\ } $$<\/div>\u3053\u308c\u3089\u306e\u57fa\u6e96\u306e\u8a3c\u660e\u306f\u3001\u300c\u5358\u8abf\u30af\u30e9\u30b9\u88dc\u984c\u300d\u306e\u30da\u30fc\u30b8\u306b\u3042\u308a\u307e\u3059\u3002<\/p><h3><span>\u72ec\u7acb\u6027\u3068\u76f8\u95a2\u6027<\/span><\/h3><p>\u72ec\u7acb\u6027\u306f\u30012 \u3064\u306e\u5909\u6570\u9593\u306e<span><a href=\"https:\/\/science-hub.click\/?p=40332\">\u5171\u5206\u6563<\/a><\/span>\u3001\u3064\u307e\u308a\u76f8\u95a2\u304c\u30bc\u30ed\u3067\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002<\/p><div><p><strong>\u5b9a\u7406<\/strong><span>\u2014<\/span> <i>X<\/i>\u3068<i>Y \u306f<\/i>\u72ec\u7acb\u3057\u3066\u3044\u307e\u3059<div class=\"math-formual notranslate\">$$ {\\Rightarrow \\operatorname{Cov}(X,Y)=\\operatorname{Corr}(X,Y)=0} $$<\/div><\/p><\/div><div><div><p>\u3053\u306e\u7279\u6027\u306f\u3001\u5171\u5206\u6563\u3092\u6b21\u306e\u3088\u3046\u306b\u8868\u73fe\u3059\u308b\u3068\u975e\u5e38\u306b\u7c21\u5358\u306b\u63a8\u5b9a\u3067\u304d\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\operatorname{cov}(X, Y) = \\operatorname{E}(X Y) &#8211; \\operatorname{E}(X)\\operatorname{E}(Y)} $$<\/div> \u3002\u3053\u308c\u307e\u3067\u898b\u3066\u304d\u305f\u3088\u3046\u306b\u3001 <i>X<\/i>\u3068<i>Y<\/i>\u306e\u72ec\u7acb\u6027\u306f\u6b21\u306e\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\operatorname{E}(X Y)= \\operatorname{E}(X)\\operatorname{E}(Y)} $$<\/div> \u3001 \u305d\u308c\u3067<div class=\"math-formual notranslate\">$$ {\\operatorname{cov}(X, Y) = \\operatorname{E}(X Y) &#8211; \\operatorname{E}(X)\\operatorname{E}(Y)=\\operatorname{E}(X)E(Y)-\\operatorname{E}(X)\\operatorname{E}(Y)=0} $$<\/div> \u3002<\/p><\/div><\/div><p>\u6b21\u306e\u4f8b\u304c\u793a\u3059\u3088\u3046\u306b\u3001\u5b9a\u7406\u306e\u9006\u306f\u507d\u3067\u3059\u3002<\/p><div><strong>\u4f8b  \uff1a<\/strong><div><p>\u3053\u306e\u4f8b\u306f\u3001Ross (2004\u3001p. 306) \u304b\u3089\u5f15\u7528\u3057\u305f\u3082\u306e\u3067\u3059\u3002<\/p><ul><li> <i>X \u3092<\/i>\u6b21\u306e\u3088\u3046\u306a\u96e2\u6563\u78ba\u7387\u5909\u6570\u3068\u3057\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ { \\mathbb{P}(X=0)=\\mathbb{P}(X=1)=\\mathbb{P}(X=-1)=\\frac{1}{3}} $$<\/div> \u3002<\/li><\/ul><ul><li> <i>X<\/i>\u306b\u95a2\u9023\u3057\u3066<i>Y \u3092<\/i>\u5b9a\u7fa9\u3057\u307e\u3057\u3087\u3046\u3002 <div class=\"math-formual notranslate\">$$ { \\begin{cases}  0 &amp; \\text{si } X\\neq 0\\\\ 1 &amp; \\text{si } X= 0\\\\ \\end{cases}} $$<\/div><\/li><\/ul><ul><li>\u8a08\u7b97\u3057\u307e\u3059<div class=\"math-formual notranslate\">$$ {\\operatorname{E}[XY]= \\frac{1}{3}(0\\cdot 1)+\\frac{1}{3}(1\\cdot 0)+\\frac{1}{3}(-1\\cdot 0)=0} $$<\/div> \u3002<\/li><\/ul><ul><li>\u79c1\u305f\u3061\u3082\u305d\u308c\u3092\u898b\u3066\u3044\u307e\u3059<div class=\"math-formual notranslate\">$$ {\\operatorname{E}[X]= \\frac{1}{3}(0)+\\frac{1}{3}(1)+\\frac{1}{3}(-1)=0+1-1=0} $$<\/div> \u3002<\/li><\/ul><ul><li>\u305d\u308c\u3067\uff1a <div class=\"math-formual notranslate\">$$ {\\operatorname{cov}(X, Y) = \\operatorname{E}(X Y) &#8211; \\operatorname{E}(X)\\operatorname{E}(Y)=0-0=0} $$<\/div> \u3002<\/li><\/ul><ul><li>\u305f\u3060\u3057\u30012 \u3064\u306e\u5909\u6570\u306f\u660e\u3089\u304b\u306b\u72ec\u7acb\u3057\u3066\u3044\u307e\u305b\u3093\u3002<\/li><\/ul><\/div><\/div><p> <i>X<\/i>\u3068<i>Y<\/i>\u9593\u306e\u7121\u76f8\u95a2\u306f\u3001\u72ec\u7acb\u6027\u3088\u308a\u3082\u5f31\u3044\u7279\u6027\u3067\u3059\u3002<i>\u5b9f\u969b\u3001<\/i><i>\u9593<\/i><i>\u306e<\/i><i>\u72ec\u7acb<\/i><i>\u6027<\/i>\u306f\u5b9a\u7fa9\u3055\u308c\u3066\u3044<i><i><i>\u307e\u3059<\/i><\/i><\/i>&#8230;)\u3002<\/p><\/div><h2 class=\"ref_link\">\u53c2\u8003\u8cc7\u6599<\/h2><ol><li><a class=\"notranslate\" href=\"https:\/\/ar.wikipedia.org\/wiki\/%D8%A7%D8%B3%D8%AA%D9%82%D9%84%D8%A7%D9%84_(%D9%86%D8%B8%D8%B1%D9%8A%D8%A9_%D8%A7%D9%84%D8%A7%D8%AD%D8%AA%D9%85%D8%A7%D9%84)\">\u0627\u0633\u062a\u0642\u0644\u0627\u0644 (\u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0627\u062d\u062a\u0645\u0627\u0644) \u2013 arabe<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/be.wikipedia.org\/wiki\/%D0%9D%D0%B5%D0%B7%D0%B0%D0%BB%D0%B5%D0%B6%D0%BD%D0%B0%D1%81%D1%86%D1%8C_(%D1%82%D1%8D%D0%BE%D1%80%D1%8B%D1%8F_%D1%96%D0%BC%D0%B0%D0%B2%D0%B5%D1%80%D0%BD%D0%B0%D1%81%D1%86%D0%B5%D0%B9)\">\u041d\u0435\u0437\u0430\u043b\u0435\u0436\u043d\u0430\u0441\u0446\u044c (\u0442\u044d\u043e\u0440\u044b\u044f \u0456\u043c\u0430\u0432\u0435\u0440\u043d\u0430\u0441\u0446\u0435\u0439) \u2013 bi\u00e9lorusse<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/ca.wikipedia.org\/wiki\/Independ%C3%A8ncia_estad%C3%ADstica\">Independ\u00e8ncia estad\u00edstica \u2013 catalan<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/cs.wikipedia.org\/wiki\/Statistick%C3%A1_nez%C3%A1vislost\">Statistick\u00e1 nez\u00e1vislost \u2013 tch\u00e8que<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/cv.wikipedia.org\/wiki\/%D0%9F%C4%83%D1%85%C4%83%D0%BD%D0%BC%D0%B0%D0%BD%D0%BB%C4%83%D1%85_(%D0%BF%D1%83%D0%BB%D0%B0%D1%8F%D1%81%D0%BB%C4%83%D1%85%D1%81%D0%B5%D0%BD_%D1%82%D0%B5%D0%BE%D1%80%D0%B8%D0%B9%C4%95)\">\u041f\u0103\u0445\u0103\u043d\u043c\u0430\u043d\u043b\u0103\u0445 (\u043f\u0443\u043b\u0430\u044f\u0441\u043b\u0103\u0445\u0441\u0435\u043d \u0442\u0435\u043e\u0440\u0438\u0439\u0115) \u2013 tchouvache<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/cy.wikipedia.org\/wiki\/Annibyniaeth_(tebygolrwydd)\">Annibyniaeth (tebygolrwydd) \u2013 gallois<\/a><\/li><\/ol><\/div>\n<div class=\"feature-video\">\n <h2>\n  \u72ec\u7acb\u6027 (\u78ba\u7387)\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\u30fb\u95a2\u9023\u52d5\u753b\n <\/h2>\n <div class=\"video-item\">\n  \n  <figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\">\n   <div class=\"wp-block-embed__wrapper\">\n    <iframe loading=\"lazy\" title=\"\u4e8b\u8c61\u306e\u72ec\u7acb\u3001\u8a66\u884c\u306e\u72ec\u7acb\u3001\u78ba\u7387\u5909\u6570\u306e\u72ec\u7acb\u3001\u306e\u5b9a\u7fa9\u3068\u9055\u3044\u3068\u95a2\u4fc2\u6027\u304c\u308f\u304b\u308b\uff01\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/e_ZFra-5_RM?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n   <\/div>\n  <\/figure>\n  \n <\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u5c0e\u5165 \u72ec\u7acb\u6027\u3068\u306f\u3001\u76f8\u4e92\u306b\u5f71\u97ff\u3092\u53ca\u307c\u3055\u306a\u3044\u30e9\u30f3\u30c0\u30e0\u306a\u30a4\u30d9\u30f3\u30c8\u3092\u76f4\u89b3\u7684\u306b\u8a8d\u5b9a\u3059\u308b\u78ba\u7387\u7684\u306a\u6982\u5ff5\u3067\u3059\u3002\u3053\u308c\u306f\u7d71\u8a08\u3084\u78ba\u7387\u8a08\u7b97\u306b\u304a\u3044\u3066\u975e\u5e38\u306b\u91cd\u8981\u306a\u6982\u5ff5\u3067\u3059\u3002 \u305f\u3068\u3048\u3070\u3001\u30b5\u30a4\u30b3\u30ed\u306e\u6700\u521d\u306e\u76ee\u306e\u5024\u306f\u30012 \u756a\u76ee\u306e\u76ee\u306e\u5024\u306b\u306f\u5f71\u97ff\u3057\u307e\u305b\u3093\u3002\u540c\u69d8 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":107480,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"https:\/\/img.youtube.com\/vi\/-06Q18suKHI\/0.jpg","fifu_image_alt":"\u72ec\u7acb\u6027 (\u78ba\u7387)\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac","footnotes":""},"categories":[5],"tags":[11,13,10,14,12,8,46281,46280,9229,16,15,9],"class_list":["post-107479","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-dictionary","tag-techniques","tag-technologie","tag-actualite","tag-news","tag-dossier","tag-definition","tag-independance","tag-independance-probabilites","tag-probabilites","tag-sciences","tag-article","tag-explications"],"_links":{"self":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/posts\/107479"}],"collection":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=107479"}],"version-history":[{"count":0,"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/posts\/107479\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/media\/107480"}],"wp:attachment":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=107479"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=107479"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=107479"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}