[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/6014#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/6014","headline":"\u30b3\u30af\u30e9\u30f3\u306e\u6587 – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2","name":"\u30b3\u30af\u30e9\u30f3\u306e\u6587 – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2","description":"before-content-x4 \u7d71\u8a08\u3067 \u30b3\u30af\u30e9\u30f3\u306e\u30bb\u30c3\u30c8 \u5206\u6563\u5206\u6790\u3067\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u3053\u306e\u6587\u306f\u3001\u30b9\u30b3\u30c3\u30c8\u30e9\u30f3\u30c9\u306e\u6570\u5b66\u8005\u30a6\u30a3\u30ea\u30a2\u30e0\u30fb\u30b8\u30a7\u30e1\u30eb\u30fb\u30b3\u30af\u30e9\u30f3\u306b\u3055\u304b\u306e\u307c\u308a\u307e\u3059\u3002 after-content-x4 \u3042\u306a\u305f\u306f\u53d7\u3051\u5165\u308c\u307e\u3059 \u306e 1\u3001 … \u306e n\u3001 {displaystyle u_ {1}\u3001dots u_ {n}\u3001} \u78ba\u304b\u306b\u72ec\u7acb\u3057\u305f\u6a19\u6e96\u6b63\u5e38\u306b\u5206\u5e03\u3057\u305f\u30e9\u30f3\u30c0\u30e0\u5909\u6570\u3067\u3042\u308a\u3001\u4ee5\u4e0b\u304c\u9069\u7528\u3055\u308c\u307e\u3059 after-content-x4 \u2211i=1nUi2= Q1+","datePublished":"2020-12-18","dateModified":"2020-12-18","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?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\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/2b629dc3e04728c0aa9ca2dfe83d829179453c6a","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/2b629dc3e04728c0aa9ca2dfe83d829179453c6a","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/6014","wordCount":5749,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4\u7d71\u8a08\u3067 \u30b3\u30af\u30e9\u30f3\u306e\u30bb\u30c3\u30c8 \u5206\u6563\u5206\u6790\u3067\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u3053\u306e\u6587\u306f\u3001\u30b9\u30b3\u30c3\u30c8\u30e9\u30f3\u30c9\u306e\u6570\u5b66\u8005\u30a6\u30a3\u30ea\u30a2\u30e0\u30fb\u30b8\u30a7\u30e1\u30eb\u30fb\u30b3\u30af\u30e9\u30f3\u306b\u3055\u304b\u306e\u307c\u308a\u307e\u3059\u3002        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u3042\u306a\u305f\u306f\u53d7\u3051\u5165\u308c\u307e\u3059 \u306e 1\u3001 … \u306e n\u3001 {displaystyle u_ {1}\u3001dots u_ {n}\u3001} \u78ba\u304b\u306b\u72ec\u7acb\u3057\u305f\u6a19\u6e96\u6b63\u5e38\u306b\u5206\u5e03\u3057\u305f\u30e9\u30f3\u30c0\u30e0\u5909\u6570\u3067\u3042\u308a\u3001\u4ee5\u4e0b\u304c\u9069\u7528\u3055\u308c\u307e\u3059        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u2211i=1nUi2= Q1+ \u22ef + Qk\u3001 {displaystyle sum _ {i = 1}^{n} u_ {i}^{2} = q_ {1} +cdots +q_ {k}\u3001} \u305d\u308c\u305e\u308c Q i{displaystyle q_ {i}} \u306e\u7dda\u5f62\u7d50\u5408\u306e\u6b63\u65b9\u5f62\u306e\u5408\u8a08 \u306e {displaystyleu} s\u8868\u73fe\u3002\u3042\u306a\u305f\u3082\u305d\u308c\u3092\u60f3\u5b9a\u3057\u3066\u3044\u307e\u3059        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4r1+ \u22ef + rk= n \u3001 {displaystyle r_ {1} +cdots +r_ {k} = n\u3001} \u3057\u305f\u304c\u3063\u3066 r i{displaystyle r_ {i}} \u306e\u30e9\u30f3\u30af Q i{displaystyle q_ {i}} \u306f\u3002\u30b3\u30af\u30e9\u30f3\u306e\u5224\u6c7a\u306f\u3001 Q i{displaystyle q_ {i}} \u30ab\u30a4\u6b63\u65b9\u5f62\u306e\u30ab\u30a4\u6b63\u65b9\u5f62\u306e\u5206\u5e03 r i{displaystyle r_ {i}} \u81ea\u7531\u306e\u8ca0\u8377\u3002 \u30b3\u30af\u30e9\u30f3\u306e\u5224\u6c7a\u306f\u3001\u30d5\u30a3\u30c3\u30b7\u30e3\u30fc\u306e\u5224\u6c7a\u306e\u9006\u8ee2\u3067\u3059\u3002 \u6edd \u30d0\u30c4 1\u3001 … \u30d0\u30c4 n\u3001 {displaystyle x_ {1}\u3001dots x_ {n}\u3001} \u4e88\u60f3\u5024\u3092\u6301\u3064\u72ec\u7acb\u3057\u305f\u6b63\u898f\u5206\u5e03\u306e\u30e9\u30f3\u30c0\u30e0\u5909\u6570 m {displaystyle mu} \u304a\u3088\u3073\u6a19\u6e96\u504f\u5dee a {displaystyle sigma} \u305d\u306e\u5f8c Ui= \uff08 Xi –  m \uff09\uff09 \/a {displaystyle u_ {i} =\uff08x_ {i} -mu\uff09\/sigma;} \u305d\u308c\u305e\u308c\u306e\u901a\u5e38\u306f\u6a19\u6e96\u3067\u3059 \u79c1 {displaystyle i} \u3002 \u3053\u308c\u3067\u3001\u4ee5\u4e0b\u3092\u66f8\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059 \u2211i=1nUi2= \u2211i=1n(Xi\u2212X\u00af\u03c3)2+ n (X\u00af\u2212\u03bc\u03c3)2{displaystyle sum _ {i = 1}^{n} u_ {i}^{2} = sum rimits _ {i = 1}^{n} left\uff08{frac {x_ {i}  –  {anuverline {x}}} {sigma}} {2} {2} {2}+nleft\uff09 mu} {sigma}}\u53f3\uff09^{2}} \u3053\u306e\u30a2\u30a4\u30c7\u30f3\u30c6\u30a3\u30c6\u30a3\u3092\u8a8d\u8b58\u3059\u308b\u306b\u306f\u3001\u4e21\u5074\u306b\u884c\u304b\u306a\u3051\u308c\u3070\u306a\u308a\u307e\u305b\u3093 a {displaystyle sigma} \u4e57\u7b97\u3057\u3001\u6b21\u306e\u3053\u3068\u304c\u9069\u7528\u3055\u308c\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044 \u2211i=1n\uff08 Xi –  m )2= \u2211i=1n\uff08 Xi –  X\u00af+ X\u00af –  m )2{displaystyle sum _ {i = 1}^{n}\uff08x_ {i} -mu\uff09^{2} = sum _ {i = 1}^{n}\uff08x_ {i}  –  {\u30aa\u30fc\u30d0\u30fc\u30e9\u30a4\u30f3{x}}+{\u30aa\u30fc\u30d0\u30fc\u30e9\u30a4\u30f3{x}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}} }}}}}}}}} \u62e1\u5f35\u3057\u3066\u8868\u793a\u3057\u307e\u3057\u305f \u2211i=1n\uff08 Xi –  X\u00af)2+ \u2211i=1n\uff08 X\u00af –  m )2+ 2 \u2211i=1n\uff08 Xi –  X\u00af\uff09\uff09 \uff08 X\u00af –  m \uff09\uff09 \u3002 {displaystyle sum _ {i = 1}^{n}\uff08x_ {i}  –  {overline {x}}\uff09^{2}+sum _ {i = 1}^{n}\uff08{overline {x}}  –  mu\uff09^{2}+2umum _ {i = 1 {i {x} {n} {n} {n} {n} {n} }}\uff09\uff08{overline {x}}  –  mu\uff09\u3002} 3\u756a\u76ee\u306e\u7528\u8a9e\u306f\u4fc2\u6570\u3067\u3042\u308b\u305f\u3081\u30bc\u30ed\u3067\u3059 \u2211i=1n\uff08 X\u00af –  Xi\uff09\uff09 = 0 {displaystyle sum _ {i = 1}^{n}\uff08{overline {x}} -x_ {i}\uff09= 0} IS\u3067\u3042\u308a\u30012\u756a\u76ee\u306e\u7528\u8a9e\u306f\u306e\u307f\u69cb\u6210\u3055\u308c\u3066\u3044\u307e\u3059 n {displaystyle n} \u307e\u3068\u3081\u3089\u308c\u305f\u540c\u4e00\u306e\u7528\u8a9e\u3002 \u4e0a\u8a18\u306e\u7d50\u679c\u3092\u7d44\u307f\u5408\u308f\u305b\u3066\u304b\u3089\u5206\u5272\u3059\u308b\u5834\u5408 a 2{displaystyle sigma ^{2}} \u3001\u305d\u308c\u304b\u3089\u3042\u306a\u305f\u306f\u53d6\u5f97\u3057\u307e\u3059\uff1a \u2211i=1n(Xi\u2212\u03bc\u03c3)2= \u2211i=1n(Xi\u2212X\u00af\u03c3)2+ n (X\u00af\u2212\u03bc\u03c3)2= Q1+ Q2\u3002 {displaystyle sum _ {i = 1}^{n}\u5de6\uff08{frac {x_ {i} -mu} {sigma}}\u53f3\uff09^{2} = sum _ {i = 1}^{n} left\uff08{frac {x_ {i}  –  {x}}}}}} {x}}}} nleft\uff08{frac {{overline {x}}  –  mu} {sigma}} right\uff09^{2} = q_ {1}+q_ {2}\u3002}} \u4eca\u304c\u30e9\u30f3\u30af\u3067\u3059 Q 2{displaystyle q_ {2}} \u308f\u305a\u304b1\uff08\u3053\u308c\u306f\u3001\u901a\u5e38\u5206\u5e03\u3057\u3066\u3044\u308b\u6a19\u6e96\u306e\u30e9\u30f3\u30c0\u30e0\u5909\u6570\u306e\u7dda\u5f62\u7d44\u307f\u5408\u308f\u305b\u306e\u6b63\u65b9\u5f62\u3067\u3059\uff09\u3002\u306e\u30e9\u30f3\u30af Q 1{displaystyle q_ {1}} \u306b\u7b49\u3057\u3044 n  –  \u521d\u3081 {displaystyle n-1} \u3001\u3057\u305f\u304c\u3063\u3066\u3001\u30b3\u30af\u30e9\u30f3\u306e\u6587\u306e\u6761\u4ef6\u304c\u6e80\u305f\u3055\u308c\u307e\u3059\u3002 \u30b3\u30af\u30e9\u30f3\u306e\u5224\u6c7a\u306f\u305d\u308c\u3092\u8a00\u3044\u307e\u3059 Q 1{displaystyle q_ {1}} \u3068 Q 2{displaystyle q_ {2}} \u30ab\u30a4\u30b9\u30af\u30a8\u30a2\u5206\u5e03\u3067\u72ec\u7acb\u3057\u3066\u3044\u307e\u3059 n  –  \u521d\u3081 {displaystyle n-1} \u3068 \u521d\u3081 {displaystyle1} \u81ea\u7531\u5ea6\u3002 \u3053\u308c\u306f\u3001\u5e73\u5747\u3068\u5206\u6563\u304c\u72ec\u7acb\u3057\u3066\u3044\u308b\u3053\u3068\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002\u3055\u3089\u306b\u9069\u7528\u3055\u308c\u307e\u3059 \uff08 X\u00af –  m )2\u301c \u03c32n\u03c712\u3002 {displaystyle\uff08{overline {x}}  –  mu\uff09^{2} sim {frac {sigma^{2}} {n}} chi _ {1}^{2}\u3002}} \u6bcd\u96c6\u56e3\u306e\u672a\u77e5\u306e\u5206\u6563\u306b a 2{displaystyle sigma ^{2}} \u611f\u8b1d\u3059\u308b\u305f\u3081\u306b\u3001\u983b\u7e41\u306b\u4f7f\u7528\u3055\u308c\u308b\u63a8\u5b9a\u5668\u304c\u4f7f\u7528\u3055\u308c\u307e\u3059 \u03c3^2= 1n\u2211i=1n(Xi\u2212X\u00af)2\u3002 {displaystyle {hat {sigma}}^{2} = {frac {1} {n}} sum _ {i = 1}^{n}\u5de6\uff08x_ {i}  –  {overline {x}} right\uff09^{2}\u3002}\u3002}\u3002 \u30b3\u30af\u30e9\u30f3\u306e\u6587\u7ae0\u306f\u305d\u308c\u3092\u793a\u3057\u3066\u3044\u307e\u3059 \u03c3^2\u301c \u03c32n\u03c7n\u221212\u3001 {displaystyle {hat {sigma}}^{2} sim {frac {sigma^{2}} {n}} chi _ {n-1}^{2}\u3001} \u306e\u671f\u5f85\u5024\u3092\u793a\u3057\u3066\u3044\u308b\u3082\u306e \u03c3^2{displaystyle {hat {sigma}}^{2}} \u5e73 a 2n\u22121n{displaystyle sigma ^{2} {frac {n-1} {n}}}} \u306f\u3002 \u4e21\u65b9\u306e\u5206\u5e03\u306f\u3001\u771f\u3067\u3042\u308b\u304c\u672a\u77e5\u306e\u5206\u6563\u306b\u6bd4\u4f8b\u3057\u307e\u3059 a 2{displaystyle sigma ^{2}} \u3057\u305f\u304c\u3063\u3066\u3001\u5f7c\u3089\u306e\u95a2\u4fc2\u306f\u72ec\u7acb\u3057\u3066\u3044\u307e\u3059 a 2{displaystyle sigma ^{2}} \u3001\u305d\u3057\u3066\u5f7c\u3089\u306f\u72ec\u7acb\u3057\u3066\u3044\u308b\u306e\u3067\u3001\u3042\u306a\u305f\u306f\u5f97\u308b (X\u00af\u2212\u03bc)21n\u2211i=1n(Xi\u2212X\u00af)2\u301c F1,n{displayStyle {frac {left\uff08{overline {x}}  –  mu\u53f3\uff09^{2}} {{frac {1} {n}} sum _ {i = 1}^{n} \u3001 \u3057\u305f\u304c\u3063\u3066 f 1,n{displaystyle f_ {1\u3001n}} f\u5206\u5e03 \u521d\u3081 {displaystyle1} \u3068 n {displaystyle n} \u81ea\u7531\u5ea6\u3092\u63cf\u5199\u3057\u307e\u3059\uff08Studensche t\u5206\u5e03\u3082\u53c2\u7167\uff09\u3002 \u30b3\u30af\u30e9\u30f3\u3001W\u3002G\u3002\uff1a \u901a\u5e38\u306e\u30b7\u30b9\u30c6\u30e0\u3067\u306e\u4e8c\u6b21\u5f62\u5f0f\u306e\u5206\u5e03\u3001\u5171\u5206\u6563\u5206\u6790\u3078\u306e\u9069\u7528 \u3002\u30b1\u30f3\u30d6\u30ea\u30c3\u30b8\u54f2\u5b66\u5354\u4f1a\u306e\u6570\u5b66\u7684\u8b70\u4e8b\u933230\uff082\uff09\uff1a178\u2013191\u30011934\u3002 \u30d0\u30d1\u30c3\u30c8\u3001R\u3002B\u3002\uff1a \u7dda\u5f62\u4ee3\u6570\u304a\u3088\u3073\u7dda\u5f62\u30e2\u30c7\u30eb \u3002\u7b2c2\u7248\u200b\u200b\uff081990\uff09\u3002\u30b9\u30d7\u30ea\u30f3\u30ac\u30fc\u3002 ISBN 978-0-387-98871-9       (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/6014#breadcrumbitem","name":"\u30b3\u30af\u30e9\u30f3\u306e\u6587 – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2"}}]}]