{"id":832,"date":"2013-06-30T16:51:25","date_gmt":"2013-06-30T07:51:25","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=832"},"modified":"2021-09-09T07:22:41","modified_gmt":"2021-09-08T22:22:41","slug":"osr201305","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/osr201305\/","title":{"rendered":"\u962a\u5927\u7406\u7cfb2013\uff1a\u7b2c5\u554f"},"content":{"rendered":"<hr \/>\n<p>\\(n\\) \u3092 \\(3\\) \u4ee5\u4e0a\u306e\u6574\u6570\u3068\u3059\u308b.\r\n\\(n\\) \u500b\u306e\u7403 \\(K _ 1 , K _ 2 , \\cdots , K _ n\\) \u3068 \\(n\\) \u500b\u306e\u7a7a\u306e\u7bb1 \\(H _ 1 , H _ 2 , \\cdots , H _ n\\) \u304c\u3042\u308b. \u4ee5\u4e0b\u306e\u3088\u3046\u306b, \\(K _ 1 , K _ 2 , \\cdots , K _ n\\) \u306e\u9806\u756a\u306b, \u7403\u3092\u7bb1\u306b \\(1\\) \u3064\u305a\u3064\u5165\u308c\u3066\u3044\u304f.\r\n\u307e\u305a, \u7403 \\(K _ 1\\) \u3092\u7bb1 \\(H _ 1 , H _ 2 , \\cdots , H _ n\\) \u306e\u3069\u308c\u304b \\(1\\) \u3064\u306b\u7121\u4f5c\u70ba\u306b\u5165\u308c\u308b. \u6b21\u306b\u7403 \\(K _ 2\\) \u3092, \u7bb1 \\(H _ 2\\) \u304c\u7a7a\u306a\u3089\u3070\u7bb1 \\(H _ 2\\) \u306b\u5165\u308c, \u7bb1 \\(H _ 2\\) \u304c\u7a7a\u3067\u306a\u3051\u308c\u3070\u6b8b\u308a\u306e \\(n-1\\) \u500b\u306e\u7a7a\u306e\u7bb1\u306e\u3069\u308c\u304b \\(1\\) \u3064\u306b\u7121\u4f5c\u70ba\u306b\u5165\u308c\u308b.\r\n\u4e00\u822c\u306b, \\(i = 2, 3, \\cdots , n\\) \u306b\u3064\u3044\u3066, \u7403 \\(K _ i\\) \u3092, \u7bb1 \\(H _ i\\) \u304c\u7a7a\u306a\u3089\u3070\u7bb1 \\(H _ i\\) \u306b\u5165\u308c, \u7bb1 \\(H _ i\\) \u304c\u7a7a\u3067\u306a\u3051\u308c\u3070\u6b8b\u308a\u306e \\(n-i+1\\) \u500b\u306e\u7a7a\u306e\u7bb1\u306e\u3069\u308c\u304b \\(1\\) \u3064\u306b\u7121\u4f5c\u70ba\u306b\u5165\u308c\u308b.<\/p>\r\n<ol>\r\n<li><p><strong>(1)<\/strong>\u3000\\(K _ n\\) \u304c\u5165\u308b\u7bb1\u306f \\(H _ 1\\) \u307e\u305f\u306f \\(H _ n\\) \u3067\u3042\u308b. \u3053\u308c\u3092\u8a3c\u660e\u305b\u3088.<\/p><\/li>\r\n<li><p><strong>(2)<\/strong>\u3000\\(K _ {n-1}\\) \u304c \\(H _ {n-1}\\) \u306b\u5165\u308b\u78ba\u7387\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n<hr \/>\r\n<!--more-->\r\n<h2>\u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n<p><strong>(1)<\/strong><\/p>\r\n<p>\u4e0e\u3048\u3089\u308c\u305f\u30eb\u30fc\u30eb\u306b\u5f93\u3048\u3070, \u7403 \\(K _ {i} \\ ( 2 \\leqq i \\leqq n )\\) \u3092\u7bb1\u306b\u5165\u308c\u7d42\u3048\u308c\u3070, \u7bb1 \\(H _ i\\) \u306f\u7a7a\u3067\u306f\u306a\u304f\u306a\u308b. \u305f\u3060\u3057, \u7bb1 \\(H _ 1\\) \u304c\u7a7a\u3067\u3042\u308b\u304b\u306f\u5b9a\u307e\u3063\u3066\u3044\u306a\u3044.<br \/>\r\n\u3057\u305f\u304c\u3063\u3066, \u7403 \\(K _ {n-1}\\) \u3092\u7bb1\u306b\u5165\u308c\u7d42\u308f\u3063\u305f\u3068\u304d, \u7a7a\u3067\u3042\u308b\u7bb1\u306f \\(H _ 1\\) \u304b \\(H _ n\\) \u3067\u3042\u308b.<br \/>\r\n\u3088\u3063\u3066, \u984c\u610f\u306f\u793a\u3055\u308c\u305f.<\/p>\r\n<p><strong>(2)<\/strong><\/p>\r\n<ol>\r\n<li>[P]\uff1a\u300c \u7403 \\(K _ {i} \\ ( 1 \\leqq i \\leqq n-1 )\\) \u3092\u7bb1\u306b\u5165\u308c\u7d42\u3048\u305f\u3068\u304d, \\(n-i+1\\) \u500b\u306e\u7bb1 \\(H _ {1}\\) \u3068 \\(H _ {i+1} , \\cdots , H _ {n}\\) \u306e\u3046\u3061 \\(1\\) \u3064\u3060\u3051\u306b\u7403\u304c\u5165\u3063\u3066\u3044\u308b. \u5404\u7bb1\u304c\u7a7a\u3067\u306f\u306a\u3044\u78ba\u7387\u306f\u7b49\u3057\u304f \\(p _ i = \\dfrac{1}{n-i+1}\\) \u3067\u3042\u308b. \u300d<\/li>\r\n<\/ol>\r\n<p>\\(1 \\leqq i \\leqq n-1\\) \u306b\u3064\u3044\u3066, [P] \u304c\u6210\u7acb\u3059\u308b\u3053\u3068\u3092\u6570\u5b66\u7684\u5e30\u7d0d\u6cd5\u3092\u7528\u3044\u3066\u793a\u3059.<\/p>\r\n<ol>\r\n<li><p><strong>1*<\/strong>\u3000\\(i=1\\) \u306e\u3068\u304d<br \/>\r\n\\(n\\) \u500b\u306e\u7bb1 \\(H _ 1 , \\cdots , H _ n\\) \u305d\u308c\u305e\u308c\u306b\u3064\u3044\u3066, \u7403\u304c\u5165\u3063\u3066\u3044\u308b\u78ba\u7387\u306f, \\(\\dfrac{1}{n}\\) \u3067\u3042\u308a, [P] \u304c\u6210\u7acb\u3059\u308b.<\/p><\/li>\r\n<li><p><strong>2*<\/strong>\u3000\\(i = j \\ ( 1 \\leqq j \\leqq n-2 )\\) \u306e\u3068\u304d<br \/>\r\n[P] \u304c\u6210\u7acb\u3059\u308b\u3068\u4eee\u5b9a\u3059\u308b.\r\n\u7403 \\(K _ {j+1}\\) \u3092\u7bb1\u306b\u5165\u308c\u308b\u3068\u304d\r\n<ul>\r\n<li><p>\u7bb1 \\(H _ {j+1}\\) \u304c\u7a7a\u3067\u3042\u308c\u3070, \u7403 \\(K _ {j+1}\\) \u306f\u7bb1 \\(H _ {j+1}\\) \u306b\u5165\u308a, \u6b8b\u308a\u306e\u7bb1\u306e\u72b6\u614b\u306f\u5909\u5316\u3057\u306a\u3044.<\/p><\/li>\r\n<li><p>\u7bb1 \\(H _ {j+1}\\) \u304c\u7a7a\u3067\u306a\u3051\u308c\u3070, \u6b8b\u308a\u306e\u7a7a\u306e\u7bb1\u306e\u3044\u305a\u308c\u304b\u306b\u7403 \\(K _ {j+1}\\) \u304c\u5165\u308b.<\/p><\/li>\r\n<\/ul>\r\n\u306a\u306e\u3067, \u7403 \\(K _ {j+1}\\) \u3092\u7bb1\u306b\u5165\u308c\u7d42\u3048\u305f\u3068\u304d, \\(n-j\\) \u500b\u306e\u7bb1 \\(H _ {1}\\) \u3068 \\(H _ {j+2} , \\cdots , H _ {n}\\) \u304c\u7a7a\u3067\u306f\u306a\u3044\u78ba\u7387\u306f,\r\n\\[\\begin{align}\r\np _ {j+1} & = p _ j + \\dfrac{1}{n-j} p _ j \\\\\r\n& = \\dfrac{1}{n-j+1} \\cdot \\dfrac{n-j+1}{n-j} \\\\\r\n& = \\dfrac {1}{n-(j+1)+1} \\ .\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066, \\(i = j+1\\) \u306e\u3068\u304d\u3082 [P] \u304c\u6210\u7acb\u3059\u308b.<\/p><\/li>\r\n<\/ol>\r\n<p><strong>1*<\/strong> <strong>2*<\/strong>\u3088\u308a, \\(1 \\leqq i \\leqq n-1\\) \u306b\u3064\u3044\u3066, [P] \u304c\u6210\u7acb\u3059\u308b\u3053\u3068\u304c\u793a\u3055\u308c\u305f.<br \/>\r\n\u3057\u305f\u304c\u3063\u3066, \\(i = n-2\\) \u306e\u3068\u304d\u3092\u8003\u3048\u308b\u3068\r\n\\[\r\np _ {n-2} = \\dfrac{1}{n-(n-2)+1} = \\dfrac{1}{3} \\ .\r\n\\]\r\n\u3064\u307e\u308a, \u7403 \\(K _ {n-1}\\) \u3092\u5165\u308c\u308b\u3068\u304d\u306b, \u7bb1 \\(H _ {n-1}\\) \u304c\u7a7a\u3067\u306f\u306a\u3044\u78ba\u7387\u306f \\(\\dfrac{1}{3}\\) \u3067\u3042\u308b.<br \/>\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u78ba\u7387\u306f\r\n\\[\r\n1 -\\dfrac{1}{3} = \\underline{\\dfrac{2}{3}} \\ .\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(n\\) \u3092 \\(3\\) \u4ee5\u4e0a\u306e\u6574\u6570\u3068\u3059\u308b. \\(n\\) \u500b\u306e\u7403 \\(K _ 1 , K _ 2 , \\cdots , K _ n\\) \u3068 \\(n\\) \u500b\u306e\u7a7a\u306e\u7bb1 \\(H _ 1 , H _ 2 , \\cdots ,  &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/osr201305\/\">\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":[90],"tags":[142,111],"class_list":["post-832","post","type-post","status-publish","format-standard","hentry","category-osaka_r_2013","tag-osaka_r","tag-111"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/832","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=832"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/832\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=832"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=832"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=832"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}