{"id":1124,"date":"2015-06-22T09:42:27","date_gmt":"2015-06-22T00:42:27","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=1124"},"modified":"2021-09-09T06:42:58","modified_gmt":"2021-09-08T21:42:58","slug":"osr201405","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/osr201405\/","title":{"rendered":"\u962a\u5927\u7406\u7cfb2014\uff1a\u7b2c5\u554f"},"content":{"rendered":"
\n

\u3055\u3044\u3053\u308d\u3092\u7e70\u308a\u8fd4\u3057\u6295\u3052, \\(n\\) \u56de\u76ee\u306b\u51fa\u305f\u76ee\u3092 \\(X _ n\\) \u3068\u3059\u308b. \\(n\\) \u56de\u76ee\u307e\u3067\u306b\u51fa\u305f\u76ee\u306e\u7a4d \\(X _ 1 X _ 2 \\cdots X _ n\\) \u3092 \\(T _ n\\) \u3067\u8868\u3059.\r\n\\(T _ n\\) \u3092 \\(5\\) \u3067\u5272\u3063\u305f\u4f59\u308a\u304c \\(1\\) \u3067\u3042\u308b\u78ba\u7387\u3092 \\(p _ n\\) \u3068\u3057, \u4f59\u308a\u304c \\(2, 3, 4\\) \u306e\u3044\u305a\u308c\u304b\u3067\u3042\u308b\u78ba\u7387\u3092 \\(q _ n\\) \u3068\u3059\u308b.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(p _ n +q _ n\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(p _ {n+1}\\) \u3092 \\(p _ n\\) \u3068 \\(n\\) \u3092\u7528\u3044\u3066\u8868\u305b.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000\\(r _ n = \\left( \\dfrac{6}{5} \\right)^n p _ n\\) \u3068\u304a\u3044\u3066 \\(r _ n\\) \u3092\u6c42\u3081\u308b\u3053\u3068\u306b\u3088\u308a, \\(p _ n\\) \u3092 \\(n\\) \u306e\u5f0f\u3067\u8868\u305b.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

    \u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n

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

    \\(n\\) \u56de\u76ee\u307e\u3067, \\(5\\) \u304c\u51fa\u306a\u3051\u308c\u3070\u3088\u3044\u306e\u3067\r\n\\[\r\np _ n +q _ n = \\underline{\\left( \\dfrac{5}{6} \\right)^n} \\ .\r\n\\]\r\n

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

    \\(T _ n\\) \u3092 \\(5\\) \u3067\u5272\u3063\u305f\u4f59\u308a\u3092 \\(R _ n\\) \u3068\u304a\u304f.
    \r\n\\(R _ n = 1 , 2 , 3 , 4\\) \u306e\u305d\u308c\u305e\u308c\u306b\u3064\u3044\u3066, \\(X _ {n+1}\\) \u306b\u5fdc\u3058\u3066 \\(R _ {n+1} = 1\\) \u3068\u306a\u308b\u5834\u5408\u3092\u8abf\u3079\u308b\u3068, \u4e0b\u8868\u306e\u3088\u3046\u306b\u306a\u308b.\r\n\\[\r\n\\begin{array}{c|cccccc} X _ {n+1} & 1 & 2 & 3 & 4 & 5 & 6 \\\\ \\hline R _ n = 1 & \\circ & - & - & - & - & \\circ \\\\ \\hline R _ n = 2 & - & - & \\circ & - & - & - \\\\ \\hline R _ n = 3 & - & \\circ & - & - & - & - \\\\ \\hline R _ n = 4 & - & - & - & \\circ & - & - \\end{array}\r\n\\]\r\n\u3086\u3048\u306b\r\n\\[\\begin{align}\r\np _ {n+1} & = \\dfrac{1}{3} p _ n +\\dfrac{1}{6} \\left\\{ \\left( \\dfrac{5}{6} \\right)^n -p _ n \\right\\} \\\\\r\n& = \\underline{\\dfrac{1}{6} p _ n +\\dfrac{1}{6} \\left( \\dfrac{5}{6} \\right)^n} \\ .\r\n\\end{align}\\]\r\n

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

    (2)<\/strong> \u306e\u7d50\u679c\u306b\u5bfe\u3057\u3066, \u4e21\u8fba\u306b \\(\\left( \\dfrac{6}{5} \\right)^{n+1}\\) \u3092\u304b\u3051\u308b\u3068\r\n\\[\\begin{align}\r\nr _ {n+1} & = \\dfrac{1}{5} r _ n +\\dfrac{1}{5} \\\\\r\n\\text{\u2234} \\quad r _ {n+1} -\\dfrac{1}{4} & = \\dfrac{1}{5} \\left( r _ n -\\dfrac{1}{4} \\right) \\ .\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066, \u6570\u5217 \\(\\left\\{ r _ n -\\dfrac{1}{4} \\right\\}\\) \u306f, \u521d\u9805 \\(r _ 1 -\\dfrac{1}{4} = \\dfrac{6}{5} \\cdot \\dfrac{1}{3} -\\dfrac{1}{4} = \\dfrac{3}{20}\\) , \u516c\u6bd4 \\(\\dfrac{1}{5}\\) \u306e\u7b49\u6bd4\u6570\u5217\u306a\u306e\u3067\r\n\\[\\begin{align}\r\nr _ n -\\dfrac{1}{4} & = \\dfrac{3}{20} \\left( \\dfrac{1}{5} \\right)^{n-1} \\\\\r\n\\text{\u2234} \\quad r _ n & = \\dfrac{1}{4} +\\dfrac{3}{4} \\left( \\dfrac{1}{5} \\right)^n \\ .\r\n\\end{align}\\]\r\n\u3088\u3063\u3066\r\n\\[\r\np _ n = \\left( \\dfrac{5}{6} \\right)^n r^n = \\underline{\\dfrac{1}{4} \\left( \\dfrac{5}{6} \\right)^n +\\dfrac{3}{4} \\left( \\dfrac{1}{6} \\right)^n} \\ .\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\u3055\u3044\u3053\u308d\u3092\u7e70\u308a\u8fd4\u3057\u6295\u3052, \\(n\\) \u56de\u76ee\u306b\u51fa\u305f\u76ee\u3092 \\(X _ n\\) \u3068\u3059\u308b. \\(n\\) \u56de\u76ee\u307e\u3067\u306b\u51fa\u305f\u76ee\u306e\u7a4d \\(X _ 1 X _ 2 \\cdots X _ n\\) \u3092 \\(T _ n\\) \u3067\u8868\u3059. \\(T _ … \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":[115],"tags":[142,112],"class_list":["post-1124","post","type-post","status-publish","format-standard","hentry","category-osaka_r_2014","tag-osaka_r","tag-112"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1124","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=1124"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1124\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1124"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1124"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1124"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}