{"id":421,"date":"2012-06-04T23:43:18","date_gmt":"2012-06-04T14:43:18","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=421"},"modified":"2021-11-04T09:12:29","modified_gmt":"2021-11-04T00:12:29","slug":"htb201205","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/htb201205\/","title":{"rendered":"\u4e00\u6a4b\u59272012\uff1a\u7b2c5\u554f"},"content":{"rendered":"
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\u6700\u521d\u306b \\(1\\) \u306e\u76ee\u304c\u4e0a\u9762\u306b\u3042\u308b\u3088\u3046\u306b\u30b5\u30a4\u30b3\u30ed\u304c\u7f6e\u304b\u308c\u3066\u3044\u308b.\r\n\u305d\u306e\u5f8c, \\(4\\) \u3064\u306e\u5074\u9762\u304b\u3089 \\(1\\) \u3064\u306e\u9762\u3092\u7121\u4f5c\u70ba\u306b\u9078\u3073, \u305d\u306e\u9762\u304c\u4e0a\u9762\u306b\u306a\u308b\u3088\u3046\u306b\u7f6e\u304d\u76f4\u3059\u64cd\u4f5c\u3092 \\(n\\) \u56de\u7e70\u308a\u8fd4\u3059. \u306a\u304a, \u30b5\u30a4\u30b3\u30ed\u306e\u5411\u304b\u3044\u5408\u3046\u9762\u306e\u76ee\u306e\u6570\u306e\u548c\u306f \\(7\\) \u3067\u3042\u308b.<\/p>\r\n

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  1. (1)<\/strong>\u3000\u6700\u5f8c\u306b \\(1\\) \u306e\u76ee\u304c\u4e0a\u9762\u306b\u3042\u308b\u78ba\u7387\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\u6700\u5f8c\u306b\u4e0a\u9762\u306b\u3042\u308b\u76ee\u306e\u6570\u306e\u671f\u5f85\u5024\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

    \u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n

    (1)<\/strong><\/p>\r\n

    \\(n\\) \u56de\u306e\u64cd\u4f5c\u306e\u5f8c, \\(1, 6\\) , \u305d\u306e\u4ed6\u306e\u76ee\u304c\u4e0a\u9762\u306b\u3042\u308b\u78ba\u7387\u3092 \\(p _ n , q _ n , r _ n \\ ( n \\geqq 0 )\\) \u3068\u304a\u304f\u3068\r\n\\[\\begin{align}\r\np _ 0 & = 1 , \\ q _ 0 +r _ 0 = 0 \\\\\r\np _ n & +q _ n +r _ n = 1 \\quad ... [1]\r\n\\end{align}\\]\r\n\u307e\u305f, \\(n\\) \u56de\u5f8c\u304b\u3089 \\(n+1\\) \u56de\u5f8c\u3078\u306e\u5909\u5316\u3092\u8003\u3048\u308b\u3068\r\n\\[\r\n\\left\\{\\begin{array}{ll} p _ {n+1} = \\dfrac{1}{4} r _ n \\\\ q _ {n+1} = \\dfrac{1}{4} r _ n \\\\ r _ {n+1} = p _ n +q _ n +\\dfrac{1}{2} r _ n \\end{array} \\right.\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066, [1] \u3092\u7528\u3044\u3066\r\n\\[\\begin{align}\r\nr _ {n+1} & =1 -r _ n +\\dfrac{1}{2} r _ {n+1} \\\\\r\n\\text{\u2234} \\quad r _ {n+1} -\\dfrac{2}{3} & = -\\dfrac{1}{2} \\left( r _ n -\\dfrac{2}{3} \\right)\r\n\\end{align}\\]\r\n\u306a\u306e\u3067\r\n\\[\\begin{align}\r\nr _ n -\\dfrac{2}{3} & =\\left( -\\dfrac{1}{2} \\right)^n \\left( r _ 0 -\\dfrac{2}{3} \\right) \\\\\r\n\\text{\u2234} \\quad r _ n & = \\dfrac{2}{3} \\left\\{ 1 - \\left( \\dfrac{1}{2} \\right)^n \\right\\}\r\n\\end{align}\\]\r\n\u3088\u3063\u3066, \\(n \\geqq 1\\) \u306b\u5bfe\u3057\u3066\r\n\\[\r\np _ n = \\dfrac{1}{4} r _ {n-1} = \\underline{\\dfrac{1}{6} \\left\\{ 1 - \\left( \\dfrac{1}{2} \\right)^{n-1} \\right\\}}\r\n\\]\r\n

    (2)<\/strong><\/p>\r\n

    \\(2\\) \uff5e \\(5\\) \u306e\u76ee\u304c\u4e0a\u9762\u306b\u306a\u308b\u78ba\u7387\u306f\u7b49\u3057\u3044\u306e\u3067, \u6c42\u3081\u308b\u671f\u5f85\u5024 \\(E\\) \u306f\r\n\\[\\begin{align}\r\nE & = 1 \\cdot p _ n +(2+3+4+5) \\cdot \\dfrac{1}{4} r _ n +6 \\cdot q _ n \\\\\r\n& = 7 p _ n +\\dfrac{7}{2} ( 1-2p _ n ) \\\\\r\n& =\\underline{\\dfrac{7}{2}}\r\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"\u6700\u521d\u306b \\(1\\) \u306e\u76ee\u304c\u4e0a\u9762\u306b\u3042\u308b\u3088\u3046\u306b\u30b5\u30a4\u30b3\u30ed\u304c\u7f6e\u304b\u308c\u3066\u3044\u308b. \u305d\u306e\u5f8c, \\(4\\) \u3064\u306e\u5074\u9762\u304b\u3089 \\(1\\) \u3064\u306e\u9762\u3092\u7121\u4f5c\u70ba\u306b\u9078\u3073, \u305d\u306e\u9762\u304c\u4e0a\u9762\u306b\u306a\u308b\u3088\u3046\u306b\u7f6e\u304d\u76f4\u3059\u64cd\u4f5c\u3092 \\(n\\) \u56de\u7e70\u308a\u8fd4\u3059. \u306a\u304a, \u30b5\u30a4\u30b3 … \u7d9a\u304d\u3092\u8aad\u3080 →<\/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":[67],"tags":[146,68],"class_list":["post-421","post","type-post","status-publish","format-standard","hentry","category-hitotsubashi_2012","tag-hitotsubashi","tag-68"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/421","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=421"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/421\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=421"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=421"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=421"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}