{"id":178,"date":"2011-12-02T22:34:19","date_gmt":"2011-12-02T13:34:19","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=178"},"modified":"2021-03-24T08:16:10","modified_gmt":"2021-03-23T23:16:10","slug":"kyr200903","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/kyr200903\/","title":{"rendered":"\u4eac\u5927\u7406\u7cfb\u4e592009\uff1a\u7b2c3\u554f"},"content":{"rendered":"<hr \/>\n<p>\\(n\\) \u679a\u306e\u30ab\u30fc\u30c9\u3092\u7a4d\u3093\u3060\u5c71\u304c\u3042\u308a, \u5404\u30ab\u30fc\u30c9\u306b\u306f\u4e0a\u304b\u3089\u9806\u756a\u306b \\(1\\) \u304b\u3089 \\(n\\) \u307e\u3067\u756a\u53f7\u304c\u3064\u3051\u3089\u308c\u3066\u3044\u308b.\r\n\u305f\u3060\u3057, \\(n \\geqq 2\\) \u3068\u3059\u308b. \u3053\u306e\u30ab\u30fc\u30c9\u306e\u5c71\u306b\u5bfe\u3057\u3066\u6b21\u306e\u8a66\u884c\u3092\u7e70\u308a\u8fd4\u3059. \\(1\\) \u56de\u306e\u8a66\u884c\u3067\u306f, \u4e00\u756a\u4e0a\u306e\u30ab\u30fc\u30c9\u3092\u53d6\u308a,\r\n\u5c71\u306e\u4e00\u756a\u4e0a\u306b\u3082\u3069\u3059\u304b, \u3042\u308b\u3044\u306f\u3044\u305a\u308c\u304b\u306e\u30ab\u30fc\u30c9\u306e\u4e0b\u306b\u5165\u308c\u308b\u3068\u3044\u3046\u64cd\u4f5c\u3092\u884c\u3046.\r\n\u3053\u308c\u3089 \\(n\\) \u901a\u308a\u306e\u64cd\u4f5c\u306f\u3059\u3079\u3066\u540c\u3058\u78ba\u7387\u3067\u3042\u308b\u3068\u3059\u308b.\r\n\\(n\\) \u56de\u306e\u8a66\u884c\u3092\u7d42\u3048\u305f\u3068\u304d, \u6700\u521d\u4e00\u756a\u4e0b\u306b\u3042\u3063\u305f\u30ab\u30fc\u30c9\uff08\u756a\u53f7 \\(n\\) \uff09\u304c\u5c71\u306e\u4e00\u756a\u4e0a\u306b\u304d\u3066\u3044\u308b\u78ba\u7387\u3092\u6c42\u3081\u3088.<\/p>\r\n<hr>\r\n<!--more-->\r\n<h4>\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n<p>\\(1\\) \u56de\u306e\u8a66\u884c\u3067, \u30ab\u30fc\u30c9\u306e\u4f4d\u7f6e\u306e\u5909\u5316\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3042\u308b.<\/p>\r\n<ul>\r\n<li><p>\u4e00\u756a\u4e0a\u306b\u3042\u308b\u3068\u304d<br \/>\r\n\u78ba\u7387 \\(\\dfrac{1}{n}\\) \u3067, \u4e0a\u304b\u3089 \\(k\\) \uff08 \\(1 \\leqq k \\leqq n\\) \uff09\u756a\u76ee\u306b\u306a\u308b.<\/p><\/li>\r\n<li><p>\u4e0a\u304b\u3089 \\(k \\ ( 2 \\leqq k \\leqq n )\\) \u756a\u76ee\u306b\u3042\u308b\u3068\u304d<br \/>\r\n\u78ba\u7387 \\(\\dfrac{k}{n}\\) \u3067\u305d\u306e\u307e\u307e, \u78ba\u7387 \\(\\dfrac{n-k}{n}\\) \u3067\u4e0a\u304b\u3089 \\(k-1\\) \u756a\u76ee\u306b\u306a\u308b.<\/p><\/li>\r\n<\/ul>\r\n<p>\u30ab\u30fc\u30c9\u304c\u4e0a\u306b\u4e0a\u304c\u308b\u306e\u306f, \\(1\\) \u56de\u306e\u8a66\u884c\u3067\u591a\u304f\u3066\u3082 \\(1\\) \u679a\u5206\u3060\u3051\u306a\u306e\u3067,\r\n\u4ee5\u4e0b\u306e \\(2\\) \u901a\u308a\u306e\u756a\u53f7 \\(n\\) \u306e\u30ab\u30fc\u30c9\u306e\u79fb\u52d5\u306b\u3064\u3044\u3066\u8003\u3048\u308c\u3070\u3088\u3044.<\/p>\r\n<ol>\r\n<li><p><strong>1*<\/strong>\u3000\\(n-1\\) \u56de\u76ee\u306b\u4e00\u756a\u4e0a\u3068\u306a\u308a, \\(n\\) \u56de\u76ee\u306e\u5f8c\u3082, \u4e00\u756a\u4e0a\u306b\u306a\u308b.<\/p><\/li>\r\n<li><p><strong>2*<\/strong>\u3000\\(k \\ ( 1 \\leqq k \\leqq n-1 )\\) \u56de\u76ee\u306e\u307f\u4f4d\u7f6e\u304c\u5909\u5316\u305b\u305a, \\(n\\) \u56de\u76ee\u306b\u4e00\u756a\u4e0a\u3068\u306a\u308b.<\/p><\/li>\r\n<\/ol>\r\n<p><strong>1*<\/strong> <strong>2*<\/strong>\u305d\u308c\u305e\u308c\u306e\u78ba\u7387\u3092 \\(P _ 1 , P _ 2\\) \u3068\u304a\u304f\u3068\r\n\\[\\begin{align}\r\nP _ 1 & = \\dfrac{1}{n} \\cdots \\dfrac{n-1}{n} \\cdot \\dfrac{1}{n} \\\\\r\n& = \\dfrac{(n-1)!}{n^n} , \\\\\r\nP _ 2 & = \\textstyle\\sum\\limits _ {k=1}^{n-1} \\dfrac{1}{n} \\cdots \\dfrac{k-1}{n} \\cdot \\dfrac{n-k}{n} \\cdot \\dfrac{k}{n} \\cdots \\dfrac{n-1}{n} \\\\\r\n& = \\dfrac{1}{n} \\cdots \\dfrac{n-1}{n} \\cdot \\dfrac{1}{n} \\textstyle\\sum\\limits _ {k=1}^{n-1} (n-k) \\\\\r\n& = \\dfrac{(n-1)!}{n^n} \\textstyle\\sum\\limits _ {k=1}^{n-1} k \\\\\r\n& = \\dfrac{(n-1)!}{n^n} \\cdot \\dfrac{n(n-1)}{2}\r\n\\end{align}\\]\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u78ba\u7387 \\(P\\) \u306f\r\n\\[\r\nP = P _ 1 +P _ 2 = \\underline{\\dfrac{(n-1)! \\left( n^2-n+2 \\right)}{2 n^n}}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(n\\) \u679a\u306e\u30ab\u30fc\u30c9\u3092\u7a4d\u3093\u3060\u5c71\u304c\u3042\u308a, \u5404\u30ab\u30fc\u30c9\u306b\u306f\u4e0a\u304b\u3089\u9806\u756a\u306b \\(1\\) \u304b\u3089 \\(n\\) \u307e\u3067\u756a\u53f7\u304c\u3064\u3051\u3089\u308c\u3066\u3044\u308b. \u305f\u3060\u3057, \\(n \\geqq 2\\) \u3068\u3059\u308b. \u3053\u306e\u30ab\u30fc\u30c9\u306e\u5c71\u306b\u5bfe\u3057\u3066\u6b21\u306e\u8a66\u884c\u3092\u7e70\u308a\u8fd4\u3059. \\ &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/kyr200903\/\">\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":[21],"tags":[140,15],"class_list":["post-178","post","type-post","status-publish","format-standard","hentry","category-kyoto_r_2009","tag-kyoto_r","tag-15"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/178","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=178"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/178\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=178"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=178"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=178"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}