$V(X+Y)=V(X)+V(Y)$\u3068\u306a\u308b\u304b\u3092\u8003\u3048\u3066\u307f\u307e\u3059\u3002<\/p>\n\n\n\n
\\[V(X+Y)=E(\\{(X+Y)-(\u03bcx+\u03bcy)\\}^2)\u3000\u3000\u2026(1)\\]<\/p>\n\n\n\n
\u5206\u6563\u306f\u3001\u78ba\u7387\u5909\u6570\u3068\u5e73\u5747\u306e\u5dee\u306e\uff12\u4e57\u3067\u3042\u308b\u305f\u3081\u3001(1)\u306e\u5f0f\u3068\u306a\u308a\u307e\u3059\u3002\u3053\u308c\u3092\u5c55\u958b\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n\n\n\n
$=E(\\{(X-\u03bcx)+(Y-\u03bcy)\\}^2)$
$=E((X-\u03bcx)^2)+2E((X-\u03bcx)(Y-\u03bcy))+E((Y-\u03bcy)^2)$<\/p>\n\n\n\n
\u5206\u6563\u306e\u5b9a\u7fa9\u3088\u308a$E((X-\u03bcx)^2)=V(X)\u3001E((Y-\u03bcy)^2)=V(Y)$\u306a\u306e\u3067\u3001<\/p>\n\n\n\n
$=V(X)+V(Y)+2E((X-\u03bcx)(Y-\u03bcy))$
$=V(X)+V(Y)+2E(XY-X\u03bcy-Y\u03bcx+\u03bcx\u03bcy)$
$=V(X)+V(Y)+2(E(XY)-\u03bcyE(X)-\u03bcxE(Y)\u03bcx+\u03bcx\u03bcy)$<\/p>\n\n\n\n
\u78ba\u7387\u5909\u6570\u306e\u671f\u5f85\u5024\u306f\u5e73\u5747\u5024\u306b\u7b49\u3057\u3044\u306e\u3067\u3001$E(X)=\u03bcx\u3001E(Y)=\u03bcy$\u3068\u304a\u304d\u3001<\/p>\n\n\n\n
$=V(X)+V(Y)+2(E(XY)-\u03bcy\u03bcx-\u03bcx\u03bcy+\u03bcx\u03bcy)$
$=V(X)+V(Y)+2(E(XY)-\u03bcx\u03bcy)$
$=V(X)+V(Y)+2(E(XY)-E(X)E(Y))$<\/p>\n\n\n\n
$E(XY)-E(X)E(Y)$\u306f\u78ba\u7387\u5909\u6570\u304c\u72ec\u7acb\uff08\uff12\u3064\u306e\u78ba\u7387\u5909\u6570\u304c\u7121\u95a2\u4fc2\u306b\u52d5\u304f\uff09\u3067\u3042\u308c\u3070\u30bc\u30ed\u306b\u306a\u308b\u671f\u5f85\u5024\u306e\u6027\u8cea\u304c\u3042\u308b\u304b\u3089\u3001<\/p>\n\n\n\n
$=V(X)+V(Y)+2\\times0$
$=V(X)+V(Y)$<\/p>\n\n\n\n
$V(X+Y)=V(X)+V(Y)$\u3068\u306a\u308b\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3057\u305f\u3002$\u3000\u2026(2)$<\/p>\n\n\n\n
\\[V(Sn)=V(X1+X2+X3+X4\u2026Xn)\\]<\/p>\n\n\n\n
(2)\u3088\u308a\u3001<\/p>\n\n\n\n
$V(Sn)=V(X1+X2+X3+X4\u2026Xn)=V(X1)+V(X2)+V(X3)+V(X4)\u2026V(Xn)$<\/p>\n\n\n\n
\u5404\u5206\u6563\u304c\u540c\u4e00\u3068\u3044\u3046\u524d\u63d0\u3092\u7f6e\u304f\u3068\u3001<\/p>\n\n\n\n
$V(Sn)=V(X1)+V(X2)+V(X3)+V(X4)\u2026V(Xn)=nV(X)$<\/p>\n\n\n\n
\u6a19\u6e96\u504f\u5dee\u306f\u5206\u6563\u306e\u5e73\u65b9\u6839\u3092\u3068\u3063\u305f\u3082\u306e\u306a\u306e\u3067\u3001\u5e73\u65b9\u6839\u3092\u53d6\u3063\u3066\u03c3\u3092\u6c42\u3081\u308b\u3002<\/p>\n\n\n\n
$\u03c3(Sn)=\\sqrt{nV(X)}$
$=\u03c3\\times\\sqrt{n}$<\/p>\n\n\n\n
\u91d1\u878d\u5de5\u5b66\u306e\u4e00\u822c\u7684\u306a\u8868\u8a18\u306b\u3059\u308b\u3068\u3001<\/p>\n\n\n\n
$\u03c3(Rt)=\u03c3\\times\\sqrt{t}$<\/p>\n\n\n\n
\u3053\u306e\u5f0f\u306f\u611f\u899a\u3068\u3082\u4e00\u81f4\u3057\u307e\u3059\u3002\u77ed\u671f\u9593\u3067\u682a\u4fa1\u304c\u5927\u304d\u304f\u5909\u52d5\u3059\u308b\u3053\u3068\u306f\u591a\u304f\u3042\u308a\u307e\u305b\u3093\u304c\u3001\u9577\u3044\u671f\u9593\u3067\u8003\u3048\u3089\u308c\u3070\u5927\u304d\u306a\u5909\u52d5\u3082\u73cd\u3057\u304f\u3042\u308a\u307e\u305b\u3093\u3002<\/p>\n\n\n\n
<\/p>\n\n\n\n
\u30dc\u30e9\u30c6\u30a3\u30ea\u30c6\u30a3\u306f\u3001\u4e00\u822c\u306b\u300c\u682a\u4fa1\u306e\u5909\u52d5\u7387\u306e\u6a19\u6e96\u504f\u5dee\u306e\u5e74\u7387\u300d\u3068\u3055\u308c\u3066\u304a\u308a\u307e\u3059\u306e\u3067\u3001\u6708\u6b21\u306e\u682a\u4fa1\u30c7\u30fc\u30bf\u304b\u3089\u6a19\u6e96\u504f\u5dee\u3092\u8a08\u7b97\u3057\u305f\u5834\u5408\u3001$\\sqrt{12}$\u3092\u639b\u3051\u3066\u30dc\u30e9\u30c6\u30a3\u30ea\u30c6\u30a3\u3092\u7b97\u51fa\u3057\u307e\u3059\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"
\u5fc5\u8981\u306a\u524d\u63d0\u77e5\u8b58 \u5206\u6563\u306e\u6027\u8cea $V(X+Y)=V(X)+V(Y)$\u3068\u306a\u308b\u304b\u3092\u8003\u3048\u3066\u307f\u307e\u3059\u3002 \\[V(X+Y)=E(\\{(X+Y)-(\u03bcx+\u03bcy)\\}^2)\u3000\u3000\u2026(1)\\] \u5206\u6563\u306f\u3001\u78ba\u7387\u5909\u6570\u3068\u5e73\u5747\u306e\u5dee\u306e\uff12\u4e57\u3067\u3042\u308b\u305f\u3081\u3001(1) […]<\/p>\n","protected":false},"author":1,"featured_media":20,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"swell_btn_cv_data":"","footnotes":""},"categories":[27],"tags":[],"class_list":["post-4492","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-27"],"_links":{"self":[{"href":"https:\/\/aiknot.jp\/media-top\/index.php?rest_route=\/wp\/v2\/posts\/4492","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/aiknot.jp\/media-top\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/aiknot.jp\/media-top\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/aiknot.jp\/media-top\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/aiknot.jp\/media-top\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4492"}],"version-history":[{"count":54,"href":"https:\/\/aiknot.jp\/media-top\/index.php?rest_route=\/wp\/v2\/posts\/4492\/revisions"}],"predecessor-version":[{"id":4721,"href":"https:\/\/aiknot.jp\/media-top\/index.php?rest_route=\/wp\/v2\/posts\/4492\/revisions\/4721"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/aiknot.jp\/media-top\/index.php?rest_route=\/wp\/v2\/media\/20"}],"wp:attachment":[{"href":"https:\/\/aiknot.jp\/media-top\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4492"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/aiknot.jp\/media-top\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4492"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/aiknot.jp\/media-top\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4492"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}