[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki18\/archives\/285742#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki18\/archives\/285742","headline":"\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u306e\u4e0d\u7b49\u5f0f – Wikipedia","name":"\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u306e\u4e0d\u7b49\u5f0f – Wikipedia","description":"\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u306e\u4e0d\u7b49\u5f0f\uff08\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u306e\u3075\u3068\u3046\u3057\u304d\u3001\u82f1: Chebyshev’s inequality\uff09\u306f\u3001\u4e0d\u7b49\u5f0f\u3067\u8868\u3055\u308c\u308b\u3001\u78ba\u7387\u8ad6\u306e\u57fa\u672c\u7684\u306a\u5b9a\u7406\u3067\u3042\u308b\u3002\u30d1\u30d5\u30cc\u30c6\u30a3\u30fb\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u306b\u3088\u3063\u3066\u521d\u3081\u3066\u8a3c\u660e\u3055\u308c\u305f\u3002 \u6a19\u672c\u307e\u305f\u306f\u78ba\u7387\u5206\u5e03\u306f\u3001\u5e73\u5747\u306e\u5468\u308a\u306b\u3001\u3042\u308b\u6a19\u6e96\u504f\u5dee\u3092\u3082\u3063\u3066\u5206\u5e03\u3059\u308b\u3002\u3053\u306e\u5206\u5e03\u3068\u6a19\u6e96\u504f\u5dee\u3068\u306e\u9593\u306e\u3001\u3069\u306e\u3088\u3046\u306a\u6a19\u672c\u30fb\u78ba\u7387\u5206\u5e03\u3067\u3082\u6210\u308a\u7acb\u3064\u95a2\u4fc2\u3092\u793a\u3057\u305f\u306e\u304c\u3001\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u306e\u4e0d\u7b49\u5f0f\u3067\u3042\u308b\u3002\u4f8b\u3048\u3070\u3001\u5e73\u5747\u304b\u3089\u6a19\u6e96\u504f\u5dee\u306e 2 \u500d\u4ee5\u4e0a\u96e2\u308c\u305f\u5024\u306f\u3001\u5168\u4f53\u306e 1\/4 \u4ee5\u4e0b\u3067\u3042\u308b\u3002\u4e00\u822c\u306b\u3001\u6a19\u6e96\u504f\u5dee\u306e n \u500d\u4ee5\u4e0a\u96e2\u308c\u305f\u5024\u306f\u5168\u4f53\u306e 1\/n2 \u4ee5\u4e0b\u3067\u3042\u308b\u3002 \u3053\u306e\u5b9a\u7406\u306f\u30ed\u30b7\u30a2\u306e\u6570\u5b66\u8005\u30d1\u30d5\u30cc\u30c6\u30a3\u30fb\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u306e\u540d\u3092\u3064\u3051\u3089\u308c\u3066\u3044\u308b\u304c\u3001\u6700\u521d\u306b\u3053\u306e\u5b9a\u7406\u3092\u793a\u3057\u305f\u306e\u306f\u5f7c\u306e\u53cb\u4eba\u3067\u3042\u308a\u540c\u50da\u3067\u3082\u3042\u3063\u305fIr\u00e9n\u00e9e-Jules Bienaym\u00e9\u3067\u3042\u308b[1]:98\u3002 \u3053\u306e\u5b9a\u7406\u306f\u6700\u521d\u306b1853\u5e74\u306b Bienaym\u00e9 \u306b\u3088\u3063\u3066\u8a3c\u660e\u304c\u306a\u3044\u72b6\u614b\u3067\u5b9a\u5f0f\u5316\u3055\u308c[2]\u3001\u5f8c\u306e1867\u5e74\u306b\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u306b\u3088\u3063\u3066\u8a3c\u660e\u3055\u308c\u305f[3] \u3002\u5f7c\u306e\u6559\u3048\u5b50\u3067\u3042\u308b\u30a2\u30f3\u30c9\u30ec\u30a4\u30fb\u30de\u30eb\u30b3\u30d5\u306f\u30011884\u5e74\u306b\u535a\u58eb\u8ad6\u6587\u306e\u4e2d\u3067\u5225\u8a3c\u660e\u3092\u4e0e\u3048\u305f[4]\u3002 Table of","datePublished":"2022-04-14","dateModified":"2022-04-14","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/jp\/wiki18\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/jp\/wiki18\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/11\/book.png","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/11\/book.png","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/ee0a68ef9839a78b1caa2b604647ff5196a6f4ac","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/ee0a68ef9839a78b1caa2b604647ff5196a6f4ac","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/jp\/wiki18\/archives\/285742","about":["Wiki"],"wordCount":3380,"articleBody":"\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u306e\u4e0d\u7b49\u5f0f\uff08\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u306e\u3075\u3068\u3046\u3057\u304d\u3001\u82f1: Chebyshev’s inequality\uff09\u306f\u3001\u4e0d\u7b49\u5f0f\u3067\u8868\u3055\u308c\u308b\u3001\u78ba\u7387\u8ad6\u306e\u57fa\u672c\u7684\u306a\u5b9a\u7406\u3067\u3042\u308b\u3002\u30d1\u30d5\u30cc\u30c6\u30a3\u30fb\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u306b\u3088\u3063\u3066\u521d\u3081\u3066\u8a3c\u660e\u3055\u308c\u305f\u3002  \u6a19\u672c\u307e\u305f\u306f\u78ba\u7387\u5206\u5e03\u306f\u3001\u5e73\u5747\u306e\u5468\u308a\u306b\u3001\u3042\u308b\u6a19\u6e96\u504f\u5dee\u3092\u3082\u3063\u3066\u5206\u5e03\u3059\u308b\u3002\u3053\u306e\u5206\u5e03\u3068\u6a19\u6e96\u504f\u5dee\u3068\u306e\u9593\u306e\u3001\u3069\u306e\u3088\u3046\u306a\u6a19\u672c\u30fb\u78ba\u7387\u5206\u5e03\u3067\u3082\u6210\u308a\u7acb\u3064\u95a2\u4fc2\u3092\u793a\u3057\u305f\u306e\u304c\u3001\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u306e\u4e0d\u7b49\u5f0f\u3067\u3042\u308b\u3002\u4f8b\u3048\u3070\u3001\u5e73\u5747\u304b\u3089\u6a19\u6e96\u504f\u5dee\u306e 2 \u500d\u4ee5\u4e0a\u96e2\u308c\u305f\u5024\u306f\u3001\u5168\u4f53\u306e 1\/4 \u4ee5\u4e0b\u3067\u3042\u308b\u3002\u4e00\u822c\u306b\u3001\u6a19\u6e96\u504f\u5dee\u306e n \u500d\u4ee5\u4e0a\u96e2\u308c\u305f\u5024\u306f\u5168\u4f53\u306e 1\/n2 \u4ee5\u4e0b\u3067\u3042\u308b\u3002\u3053\u306e\u5b9a\u7406\u306f\u30ed\u30b7\u30a2\u306e\u6570\u5b66\u8005\u30d1\u30d5\u30cc\u30c6\u30a3\u30fb\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u306e\u540d\u3092\u3064\u3051\u3089\u308c\u3066\u3044\u308b\u304c\u3001\u6700\u521d\u306b\u3053\u306e\u5b9a\u7406\u3092\u793a\u3057\u305f\u306e\u306f\u5f7c\u306e\u53cb\u4eba\u3067\u3042\u308a\u540c\u50da\u3067\u3082\u3042\u3063\u305fIr\u00e9n\u00e9e-Jules Bienaym\u00e9\u3067\u3042\u308b[1]:98\u3002\u3053\u306e\u5b9a\u7406\u306f\u6700\u521d\u306b1853\u5e74\u306b Bienaym\u00e9 \u306b\u3088\u3063\u3066\u8a3c\u660e\u304c\u306a\u3044\u72b6\u614b\u3067\u5b9a\u5f0f\u5316\u3055\u308c[2]\u3001\u5f8c\u306e1867\u5e74\u306b\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u306b\u3088\u3063\u3066\u8a3c\u660e\u3055\u308c\u305f[3] \u3002\u5f7c\u306e\u6559\u3048\u5b50\u3067\u3042\u308b\u30a2\u30f3\u30c9\u30ec\u30a4\u30fb\u30de\u30eb\u30b3\u30d5\u306f\u30011884\u5e74\u306b\u535a\u58eb\u8ad6\u6587\u306e\u4e2d\u3067\u5225\u8a3c\u660e\u3092\u4e0e\u3048\u305f[4]\u3002  Table of Contents\u4e00\u822c\u7684\u8868\u73fe[\u7de8\u96c6]\u6e2c\u5ea6\u8ad6\u7684\u8868\u73fe[\u7de8\u96c6]\u78ba\u7387\u8ad6\u7684\u8868\u73fe[\u7de8\u96c6]\u4f8b[\u7de8\u96c6]\u6e2c\u5ea6\u8ad6\u7684\u306a\u8a3c\u660e[\u7de8\u96c6]\u78ba\u7387\u8ad6\u7684\u306a\u8a3c\u660e[\u7de8\u96c6]\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]\u4e00\u822c\u7684\u8868\u73fe[\u7de8\u96c6]\u3053\u306e\u4e0d\u7b49\u5f0f\u306f\u6e2c\u5ea6\u8ad6\u3092\u4f7f\u3063\u3066\u4e00\u822c\u7684\u306b\u8ff0\u3079\u308b\u3053\u3068\u304c\u3067\u304d\u3001\u305d\u308c\u304b\u3089\u7279\u5225\u306e\u5834\u5408\uff08\u6e2c\u5ea6\u7a7a\u9593\u306e\u6b21\u5143\u304c 1\uff09\u3068\u3057\u3066\u3001\u78ba\u7387\u8ad6\u3067\u306e\u5f62\u304c\u5c0e\u304b\u308c\u308b\u3002\u6e2c\u5ea6\u8ad6\u7684\u8868\u73fe[\u7de8\u96c6](X, \u03a3, \u03bc) \u3092\u6e2c\u5ea6\u7a7a\u9593\u3001f \u3092 X \u4e0a\u3067\u5b9a\u7fa9\u3055\u308c\u305f\u62e1\u5f35\u5b9f\u6570\uff08\u7121\u9650\u5927\u3092\u542b\u3080\uff09\u5024\u53ef\u6e2c\u95a2\u6570\u3068\u3059\u308b\u3068\u3001\u4efb\u610f\u306e\u5b9f\u6570 t > 0 \u306b\u5bfe\u3057\u3066  \u03bc({x\u2208X:|f(x)|\u2265t})\u22641t2\u222bXf2d\u03bc{displaystyle mu ({xin X,:,,|f(x)|geq t})leq {1 over t^{2}}int _{X}f^{2},dmu }\u3068\u306a\u308b\u3002\u3088\u308a\u4e00\u822c\u7684\u306b\u306f\u3001g \u304c\u975e\u8ca0\u5b9f\u6570\u5024\u53ef\u6e2c\u95a2\u6570\u3067\u3001f \u306e\u7bc4\u56f2\u3067\u6e1b\u5c11\u3057\u306a\u3044\u3068\u3059\u308c\u3070\u3001\u03bc({x\u2208X:f(x)\u2265t})\u22641g(t)\u222bXg\u2218fd\u03bc{displaystyle mu ({xin X,:,,f(x)geq t})leq {1 over g(t)}int _{X}gcirc f,dmu }\u3068\u306a\u308b\u3002\u6700\u521d\u306e\u5f0f\u306f\u3001\u3053\u3053\u3067 g(t) \u3092g(t)={t2if\u00a0\u00a0\u00a0t\u226500otherwise{displaystyle g(t)={begin{cases}t^{2}&{mbox{if}}~~~tgeq 0\\0&{mbox{otherwise}}end{cases}}}\u3067\u5b9a\u7fa9\u3057\u3001f \u306e\u4ee3\u308f\u308a\u306b |f| \u3092\u7528\u3044\u308c\u3070\u5c0e\u304b\u308c\u308b\u3002\u78ba\u7387\u8ad6\u7684\u8868\u73fe[\u7de8\u96c6]X \u3092\u3001\u671f\u5f85\u5024\u304c \u03bc, \u6709\u9650\u306e\u5206\u6563\u304c \u03c32 \u3067\u3042\u308b\u78ba\u7387\u5909\u6570\u3068\u3059\u308b\u3068\u3001\u4efb\u610f\u306e\u5b9f\u6570 k > 0 \u306b\u5bfe\u3057\u3066Pr(|X\u2212\u03bc|\u2265k\u03c3)\u22641k2{displaystyle Pr(left|X-mu right|geq ksigma )leq {frac {1}{k^{2}}}}\u305f\u3060\u3057 k > 1 \u306e\u5834\u5408\u306b\u3060\u3051\u610f\u5473\u304c\u3042\u308b\u3002\u4f59\u4e8b\u8c61\u306b\u3064\u3044\u3066\u3001\u3053\u3046\u306a\u308b\u3002"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki18\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki18\/archives\/285742#breadcrumbitem","name":"\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u306e\u4e0d\u7b49\u5f0f – Wikipedia"}}]}]