{"id":1853,"date":"2021-09-05T20:51:51","date_gmt":"2021-09-05T11:51:51","guid":{"rendered":"https:\/\/www.roundown.net\/nyushi\/?p=1853"},"modified":"2021-09-12T09:04:20","modified_gmt":"2021-09-12T00:04:20","slug":"ngr201603","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/ngr201603\/","title":{"rendered":"\u540d\u53e4\u5c4b\u5927\u7406\u7cfb2016\uff1a\u7b2c3\u554f"},"content":{"rendered":"
\n

\u7389\u304c \\(2\\) \u500b\u305a\u3064\u5165\u3063\u305f \\(2\\) \u3064\u306e\u888b A , B \u304c\u3042\u308b\u3068\u304d, \u888b B \u304b\u3089\u7389\u3092 \\(1\\) \u500b\u53d6\u308a\u51fa\u3057\u3066\u888b A \u306b\u5165\u308c, \u6b21\u306b\u888b A \u304b\u3089\u7389\u3092 \\(1\\) \u500b\u53d6\u308a\u51fa\u3057\u3066\u888b B \u306b\u5165\u308c\u308b, \u3068\u3044\u3046\u64cd\u4f5c\u3092 \\(1\\) \u56de\u306e\u64cd\u4f5c\u3068\u6570\u3048\u308b\u3053\u3068\u306b\u3059\u308b. A \u306b\u8d64\u7389\u304c \\(2\\) \u500b, B \u306b\u767d\u7389\u304c \\(2\\) \u500b\u5165\u3063\u305f\u72b6\u614b\u304b\u3089\u59cb\u3081, \u3053\u306e\u64cd\u4f5c\u3092 \\(n\\) \u56de\u7e70\u308a\u8fd4\u3057\u305f\u5f8c\u306b\u888b B \u306b\u5165\u3063\u3066\u3044\u308b\u8d64\u7389\u306e\u500b\u6570\u304c \\(k\\) \u500b\u3067\u3042\u308b\u78ba\u7387\u3092 \\(P _ n (k) \\ ( n = 1, 2, 3, \\cdots )\\) \u3068\u3059\u308b. \u3053\u306e\u3068\u304d, \u6b21\u306e\u554f\u306b\u7b54\u3048\u3088.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(k = 0, 1, 2\\) \u306b\u5bfe\u3059\u308b \\(P _ 1 (k)\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(k = 0, 1, 2\\) \u306b\u5bfe\u3059\u308b \\(P _ n (k)\\) \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

    \u888b B \u306b\u8d64\u7389\u304c \\(k\\) \u500b\u5165\u3063\u3066\u3044\u308b\u72b6\u614b\u3092 \\(S_k \\ ( k = 0 , 1 , 2 )\\) \u3068\u304a\u304f.
    \r\n\\(S_0 , S_1 , S_2\\) \u304b\u3089\u306e \\(1\\) \u56de\u306e\u64cd\u4f5c\u3092\u884c\u3046\u3068, \u305d\u308c\u305e\u308c\u4e0b\u56f3\u306b\u793a\u3059\u78ba\u7387\u3067\u9077\u79fb\u3059\u308b.<\/p>\r\n\"\"\r\n

    \u3086\u3048\u306b, \\(n \\geqq 0\\) \u306b\u5bfe\u3057\u3066\r\n\\[\\begin{align}\r\nP_ {n+1} (0) & = \\dfrac{1}{3} P_n (0) & +\\dfrac{1}{6} P_n (1) & \\quad & \\quad ... [1] \\ , \\\\\r\nP_ {n+1} (1) & = \\dfrac{2}{3} P_n (0) & +\\dfrac{2}{3} P_n (1) & +\\dfrac{2}{3} P_n (2) & \\quad ... [2] \\ , \\\\\r\nP_ {n+1} (2) & = \\quad & +\\dfrac{1}{6} P_n (1) & +\\dfrac{1}{3 } P_n (2) & \\quad ... [3] \\ .\r\n\\end{align}\\]\r\n[2] \u3088\u308a, \\(n\\geq 1\\) \u306b\u3064\u3044\u3066\r\n\\[\r\nP_n (1) = \\dfrac{2}{3} \\quad ( \\ \\text{\u2235} \\ P_n (0) +P_n (1) +P_n (2) = 1 \\ ) \\quad ... [4] \\ .\r\n\\]\r\n\u521d\u3081\u306e\u72b6\u614b\u304b\u3089, \\(P_0 (0) = 1\\) , \\(P_0 (1) = P_0 (2) = 0\\) \u306a\u306e\u3067, [1] \uff5e [3] \u3088\u308a\r\n\\[\r\nP_1 (0) = \\underline{\\dfrac{1}{3}} , \\ P_1 (1) = \\underline{\\dfrac{2}{3}} , \\ P_1 (2) = \\underline{0} \\ .\r\n\\]\r\n

    (2)<\/strong><\/p>\r\n[4] \u3088\u308a\r\n\\[\r\nP_n (1) = \\underline{\\dfrac{2}{3}} \\ .\r\n\\]\r\n[1] , [4] \u3088\u308a\r\n\\[\\begin{align}\r\nP_ {n+1} (0) & = \\dfrac{1}{3} P_n (0) +\\dfrac{1}{6} \\cdot \\dfrac{2}{3} \\\\\r\n\\text{\u2234} \\quad P_ {n+1} (0) -\\dfrac{1}{6} & = -\\dfrac{1}{3} \\left( P_n (0) -\\dfrac{1}{6} \\right) \\ .\r\n\\end{align}\\]\r\n\u6570\u5217 \\(\\left\\{ P_n (0) -\\dfrac{1}{6} \\right\\}\\) \u306f, \u521d\u9805 \\(P_1 (0) -\\dfrac{1}{6} = \\dfrac{1}{6}\\) , \u516c\u6bd4 \\(\\dfrac{1}{3}\\) \u306e\u7b49\u6bd4\u6570\u5217\u306a\u306e\u3067\r\n\\[\\begin{align}\r\nP_n (0) -\\dfrac{1}{6} & = \\dfrac{1}{6} \\left( \\dfrac{1}{3} \\right)^{n-1} \\\\\r\n\\text{\u2234} \\quad P_n (0) & = \\underline{\\dfrac{1}{6} +\\dfrac{1}{2} \\left( \\dfrac{1}{3} \\right)^n} \\ .\r\n\\end{align}\\]\r\n\u307e\u305f\r\n\\[\\begin{align}\r\nP_n (2) & = 1 -P_n (0) -P_n (1) \\\\\r\n& = \\underline{\\dfrac{1}{6} -\\dfrac{1}{2} \\left( \\dfrac{1}{3} \\right)^n} \\ .\r\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"\u7389\u304c \\(2\\) \u500b\u305a\u3064\u5165\u3063\u305f \\(2\\) \u3064\u306e\u888b A , B \u304c\u3042\u308b\u3068\u304d, \u888b B \u304b\u3089\u7389\u3092 \\(1\\) \u500b\u53d6\u308a\u51fa\u3057\u3066\u888b A \u306b\u5165\u308c, \u6b21\u306b\u888b A \u304b\u3089\u7389\u3092 \\(1\\) \u500b\u53d6\u308a\u51fa\u3057\u3066\u888b B \u306b\u5165\u308c\u308b, \u3068\u3044\u3046\u64cd\u4f5c\u3092 \\ … \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":[156],"tags":[143,162],"class_list":["post-1853","post","type-post","status-publish","format-standard","hentry","category-nagoya_r_2016","tag-nagoya_r","tag-162"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1853","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=1853"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1853\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1853"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1853"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1853"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}