{"id":471,"date":"2012-11-10T22:33:53","date_gmt":"2012-11-10T13:33:53","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=471"},"modified":"2021-09-23T10:23:09","modified_gmt":"2021-09-23T01:23:09","slug":"thr201203","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/thr201203\/","title":{"rendered":"\u6771\u5317\u5927\u7406\u7cfb2012\uff1a\u7b2c3\u554f"},"content":{"rendered":"<hr \/>\n<p>\u888b A , \u888b B \u306e\u305d\u308c\u305e\u308c\u306b, \\(1\\) \u304b\u3089 \\(N\\) \u306e\u81ea\u7136\u6570\u304c\u3072\u3068\u3064\u305a\u3064\u66f8\u304b\u308c\u305f \\(N\\) \u679a\u306e\u30ab\u30fc\u30c9\u304c\u5165\u3063\u3066\u3044\u308b. \u3053\u308c\u3089\u306e\u30ab\u30fc\u30c9\u3092\u3088\u304f\u304b\u304d\u307e\u305c\u3066\u53d6\u308a\u51fa\u3057\u3066\u3044\u304f.\r\n\u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088.<\/p>\r\n<ol>\r\n<li><p><strong>(1)<\/strong>\u3000\\(N=4\\) \u3068\u3059\u308b.\r\n\u888b A , B \u306e\u305d\u308c\u305e\u308c\u304b\u3089\u540c\u6642\u306b \\(1\\) \u679a\u305a\u3064\u30ab\u30fc\u30c9\u3092\u53d6\u308a\u51fa\u3057, \u6570\u5b57\u304c\u540c\u3058\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\u3059\u308b\u64cd\u4f5c\u3092\u7e70\u308a\u8fd4\u3059.\r\n\u305f\u3060\u3057, \u53d6\u308a\u51fa\u3057\u305f\u30ab\u30fc\u30c9\u306f\u5143\u306b\u306f\u623b\u3055\u306a\u3044\u3082\u306e\u3068\u3059\u308b.\r\n\\(4\\) \u56de\u306e\u30ab\u30fc\u30c9\u306e\u53d6\u308a\u51fa\u3057\u64cd\u4f5c\u304c\u7d42\u308f\u3063\u305f\u5f8c, \u6570\u5b57\u304c\u4e00\u81f4\u3057\u3066\u3044\u305f\u56de\u6570\u3092 \\(X\\) \u3068\u3059\u308b.\r\n\\(X=1 , \\ X=2 , \\ X=3 , \\ X=4\\) \u3068\u306a\u308b\u78ba\u7387\u3092\u305d\u308c\u305e\u308c\u6c42\u3081\u3088.\r\n\u307e\u305f, \\(X\\) \u306e\u671f\u5f85\u5024\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<li><p><strong>(2)<\/strong>\u3000\\(N=3\\) \u3068\u3057, \\(n\\) \u306f\u81ea\u7136\u6570\u3068\u3059\u308b.\r\n\u888b A , B \u306e\u305d\u308c\u305e\u308c\u304b\u3089\u540c\u6642\u306b \\(1\\) \u679a\u305a\u3064\u30ab\u30fc\u30c9\u3092\u53d6\u308a\u51fa\u3057, \u30ab\u30fc\u30c9\u306e\u6570\u5b57\u304c\u4e00\u81f4\u3057\u3066\u3044\u305f\u3089, \u305d\u308c\u3089\u306e\u30ab\u30fc\u30c9\u3092\u53d6\u308a\u9664\u304d, \u4e00\u81f4\u3057\u3066\u3044\u306a\u304b\u3063\u305f\u3089, \u5143\u306e\u888b\u306b\u623b\u3059\u3068\u3044\u3046\u64cd\u4f5c\u3092\u7e70\u308a\u8fd4\u3059.\r\n\u30ab\u30fc\u30c9\u304c\u521d\u3081\u3066\u53d6\u308a\u9664\u304b\u308c\u308b\u306e\u304c \\(n\\) \u56de\u76ee\u3067\u8d77\u3053\u308b\u78ba\u7387\u3092 \\(p _ n\\) \u3068\u3057, \\(n\\) \u56de\u76ee\u306e\u64cd\u4f5c\u3067\u3059\u3079\u3066\u306e\u30ab\u30fc\u30c9\u304c\u53d6\u308a\u9664\u304b\u308c\u308b\u78ba\u7387\u3092 \\(q _ n\\) \u3068\u3059\u308b. \\(p _ n\\) \u3068 \\(q _ n\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n<hr \/>\r\n<!--more-->\r\n<h4>\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n<p><strong>(1)<\/strong><\/p>\r\n<p>\u888b A \u304b\u3089\u306f \\(1, 2, 3, 4\\) \u306e\u30ab\u30fc\u30c9\u304c\u9806\u306b\u53d6\u308a\u51fa\u3059\u3068\u8003\u3048\u3066\u3088\u3044.<br \/>\r\n\\(X=k \\ ( k= 0, 1, \\cdots , 4 )\\) \u3068\u306a\u308b\u78ba\u7387\u3092 \\(P(k)\\) \u3068\u8868\u3059.<br \/>\r\n\u888b B \u304b\u3089\u306e\u53d6\u308a\u51fa\u3057\u65b9\u306f, \\(4 {!} =24\\) \u901a\u308a\u3042\u308b.<\/p>\r\n<ol>\r\n<li><p><strong>1*<\/strong>\u3000\\(X=4\\) \u3068\u306a\u308b\u306e\u306f, \\(1\\) \u901a\u308a\u3057\u304b\u306a\u3044\u306e\u3067\r\n\\[\r\nP(4) = \\underline{\\dfrac{1}{24}}\n\\]<\/li>\r\n<li><p><strong>2*<\/strong>\u3000\\(X=3\\) \u3068\u306a\u308b\u3053\u3068\u306f\u306a\u3044\u306e\u3067\r\n\\[\r\nP(3) = \\underline{0}\n\\]<\/li>\r\n<li><p><strong>3*<\/strong>\u3000\\(X=2\\) \u3068\u306a\u308b\u306e\u306f, \u4e00\u81f4\u3059\u308b\u6570\u5b57\u306e\u9078\u3073\u65b9\u304c, \\({} _ {4} \\text{C} {} _ 2 = 6\\) \u901a\u308a\u3042\u308b\u306e\u3067\r\n\\[\r\nP(2) = \\dfrac{6}{24} = \\underline{\\dfrac{1}{4}}\n\\]<\/li>\r\n<li><p><strong>4*<\/strong>\u3000\\(X=1\\) \u3068\u306a\u308b\u306e\u306f, \u4e00\u81f4\u3059\u308b\u6570\u5b57\u306e\u9078\u3073\u65b9\u304c, \\(4\\) \u901a\u308a\u3042\u308a, \u4e00\u81f4\u3057\u306a\u3044\u6570\u5b57\u306e\u53d6\u308a\u51fa\u3057\u65b9\u306f \\(2\\) \u901a\u308a\u3042\u308b\u306e\u3067\r\n\\[\r\nP(1) = \\dfrac{4 \\cdot 2}{24} = \\underline{\\dfrac{1}{3}}\n\\]<\/li>\r\n<li><p><strong>5*<\/strong>\u3000\\(X=0\\) \u3068\u306a\u308b\u306e\u306f\r\n\\[\r\nP(0) = 1 -\\left( \\dfrac{1}{24} +\\dfrac{1}{4} +\\dfrac{1}{3} \\right) = \\dfrac{3}{8}\n\\]<\/li>\r\n<\/ol>\r\n<p>\u4ee5\u4e0a\u3088\u308a, \u6c42\u3081\u308b\u671f\u5f85\u5024 \\(E\\) \u306f\r\n\\[\\begin{align}\r\nE & = 4 \\cdot \\dfrac{1}{24} +3 \\cdot 0 +2 \\cdot \\dfrac{1}{4} +1 \\cdot \\dfrac{1}{3} +0 \\cdot \\dfrac{3}{8} \\\\\r\n& = \\underline{1}\n\\end{align}\\]\r\n<p><strong>(2)<\/strong><\/p>\r\n<p>\u888b A , B \u306b \\(k\\) \u679a\u305a\u3064\u30ab\u30fc\u30c9\u304c\u5165\u3063\u3066\u3044\u308b\u3068\u304d, \u6570\u5b57\u304c\u4e00\u81f4\u3059\u308b\u78ba\u7387\u306f \\(\\dfrac{1}{k}\\) \u3067\u3042\u308b.<br \/>\r\n\\(n\\) \u56de\u76ee\u3067\u30ab\u30fc\u30c9\u304c\u521d\u3081\u3066\u53d6\u308a\u9664\u304b\u308c\u308b\u306e\u306f, \\(n\\) \u56de\u76ee\u3067\u521d\u3081\u3066\u6570\u5b57\u304c\u4e00\u81f4\u3059\u308b\u3068\u304d\u306a\u306e\u3067\r\n\\[\r\np _ n = \\left( \\dfrac{2}{3} \\right)^{n-1} \\cdot \\dfrac{1}{3} = \\underline{\\dfrac{1}{3} \\left( \\dfrac{2}{3} \\right)^{n-1}}\n\\]\r\n\\(n\\) \u56de\u76ee\uff08 \\(n \\geqq 3\\) \uff09\u3067\u3059\u3079\u3066\u306e\u30ab\u30fc\u30c9\u304c\u53d6\u308a\u9664\u304b\u308c\u308b\u306e\u306f<\/p>\r\n<ul>\r\n<li><p>\\(k\\) \u56de\u76ee\uff08 \\(1 \\leqq k \\leqq n-2\\) \uff09\u3067\u521d\u3081\u3066\u6570\u5b57\u304c\u4e00\u81f4\u3059\u308b.<\/p><\/li>\r\n<li><p>\\(n-1\\) \u56de\u76ee\u3067 \\(2\\) \u56de\u76ee\u306b\u6570\u5b57\u304c\u4e00\u81f4\u3059\u308b.<\/p><\/li>\r\n<li><p>\\(n\\) \u56de\u76ee\u3067\u6700\u5f8c\u306e\u6570\u5b57\u304c\u4e00\u81f4\u3059\u308b\uff08\u5fc5\u305a\u4e00\u81f4\u3059\u308b\uff09.<\/p><\/li>\r\n<\/ul>\r\n<p>\u3068\u306a\u308b\u3068\u304d\u306a\u306e\u3067\r\n\\[\\begin{align}\r\nq _ n & = \\textstyle\\sum\\limits _ {k=1}^{n-2} p _ k \\cdot \\left( \\dfrac{1}{2} \\right)^{n-1-k} \\\\\r\n& = \\dfrac{1}{2^n} \\textstyle\\sum\\limits _ {k=1}^{n-2} \\left( \\dfrac{4}{3} \\right)^{k} \\\\\r\n& = \\dfrac{1}{2^n} \\cdot \\dfrac{4}{3} \\cdot \\dfrac{\\left( \\frac{4}{3} \\right)^{n-2} -1}{\\frac{4}{3} -1} \\\\\r\n& = \\left( \\dfrac{2}{3} \\right)^{n-2} -\\left( \\dfrac{1}{2} \\right)^{n-2}\n\\end{align}\\]\r\n\\(n = 1, 2\\) \u306e\u3068\u304d\u306f, \u660e\u3089\u304b\u306b \\(q _ n = 0\\) \u306a\u306e\u3067, \u4ee5\u4e0a\u3092\u307e\u3068\u3081\u3066\r\n\\[\r\nq _ n = \\underline{\\left\\{ \\begin{array}{ll} 0 & \\left( \\ n = 1, 2 \\text{\u306e\u3068\u304d} \\right) \\\\ \\left( \\dfrac{2}{3} \\right)^{n-2} -\\left( \\dfrac{1}{2} \\right)^{n-2} & \\left( \\ n \\geqq 3 \\text{\u306e\u3068\u304d} \\right) \\end{array} \\right.}\n\\]\r\n","protected":false},"excerpt":{"rendered":"\u888b A , \u888b B \u306e\u305d\u308c\u305e\u308c\u306b, \\(1\\) \u304b\u3089 \\(N\\) \u306e\u81ea\u7136\u6570\u304c\u3072\u3068\u3064\u305a\u3064\u66f8\u304b\u308c\u305f \\(N\\) \u679a\u306e\u30ab\u30fc\u30c9\u304c\u5165\u3063\u3066\u3044\u308b. \u3053\u308c\u3089\u306e\u30ab\u30fc\u30c9\u3092\u3088\u304f\u304b\u304d\u307e\u305c\u3066\u53d6\u308a\u51fa\u3057\u3066\u3044\u304f. \u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088. (1)\u3000\\(N= &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/thr201203\/\">\u7d9a\u304d\u3092\u8aad\u3080 <span class=\"meta-nav\">&rarr;<\/span><\/a>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[72],"tags":[68,148],"class_list":["post-471","post","type-post","status-publish","format-standard","hentry","category-tohoku_r_2012","tag-68","tag-tohoku_r"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/471","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/comments?post=471"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/471\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=471"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=471"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=471"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}