{"id":731,"date":"2013-04-12T08:39:27","date_gmt":"2013-04-11T23:39:27","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=731"},"modified":"2021-10-31T08:30:16","modified_gmt":"2021-10-30T23:30:16","slug":"tkb200704","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tkb200704\/","title":{"rendered":"\u6771\u5927\u6587\u7cfb2007\uff1a\u7b2c4\u554f"},"content":{"rendered":"
\n

\u8868\u304c\u51fa\u308b\u78ba\u7387\u304c \\(p\\) , \u88cf\u304c\u51fa\u308b\u78ba\u7387\u304c \\(1-p\\) \u3067\u3042\u308b\u3088\u3046\u306a\u786c\u8ca8\u304c\u3042\u308b.\r\n\u305f\u3060\u3057, \\(0 \\lt p \\lt 1\\) \u3068\u3059\u308b. \u3053\u306e\u786c\u8ca8\u3092\u6295\u3052\u3066, \u6b21\u306e\u30eb\u30fc\u30eb (R)<\/strong> \u306e\u4e0b\u3067, \u30d6\u30ed\u30c3\u30af\u7a4d\u307f\u30b2\u30fc\u30e0\u3092\u884c\u3046.<\/p>\r\n

    \r\n
  1. (R)<\/strong>\r\n
      \r\n
    1. [1]\u3000\u30d6\u30ed\u30c3\u30af\u306e\u9ad8\u3055\u306f, \u6700\u521d\u306f \\(0\\) \u3068\u3059\u308b.<\/li>\r\n
    2. [2]\u3000\u786c\u8ca8\u3092\u6295\u3052\u3066\u8868\u304c\u51fa\u308c\u3070\u9ad8\u3055 \\(1\\) \u306e\u30d6\u30ed\u30c3\u30af\u3092 \\(1\\) \u3064\u7a4d\u307f\u4e0a\u3052, \u88cf\u304c\u51fa\u308c\u3070\u30d6\u30ed\u30c3\u30af\u3092\u3059\u3079\u3066\u53d6\u308a\u9664\u3044\u3066\u9ad8\u3055 \\(0\\) \u306b\u623b\u3059.<\/li>\r\n<\/ol><\/li>\r\n<\/ol>\r\n

      \\(n\\) \u3092\u6b63\u306e\u6574\u6570, \\(m\\) \u3092 \\(0 \\leqq m \\leqq n\\) \u3092\u307f\u305f\u3059\u6574\u6570\u3068\u3059\u308b.<\/p>\r\n

        \r\n

      1. (1)<\/strong>\u3000\\(n\\) \u56de\u786c\u8ca8\u3092\u6295\u3052\u305f\u3068\u304d, \u6700\u5f8c\u306b\u30d6\u30ed\u30c3\u30af\u306e\u9ad8\u3055\u304c \\(m\\) \u3068\u306a\u308b\u78ba\u7387 \\(p _ m\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

      2. (2)<\/strong>\u3000(1)<\/strong> \u3067, \u6700\u5f8c\u306b\u30d6\u30ed\u30c3\u30af\u306e\u9ad8\u3055\u304c \\(m\\) \u4ee5\u4e0b\u3068\u306a\u308b\u78ba\u7387 \\(q _ m\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

      3. (3)<\/strong>\u3000\u30eb\u30fc\u30eb (R)<\/strong> \u306e\u4e0b\u3067, \\(n\\) \u56de\u306e\u786c\u8ca8\u6295\u3052\u3092\u72ec\u7acb\u306b \\(2\\) \u5ea6\u884c\u3044, \u305d\u308c\u305e\u308c\u6700\u5f8c\u306e\u30d6\u30ed\u30c3\u30af\u306e\u9ad8\u3055\u3092\u8003\u3048\u308b. \\(2\\) \u5ea6\u306e\u3046\u3061, \u9ad8\u3044\u65b9\u306e\u30d6\u30ed\u30c3\u30af\u306e\u9ad8\u3055\u304c \\(m\\) \u3067\u3042\u308b\u78ba\u7387 \\(r _ m\\) \u3092\u6c42\u3081\u3088. \u305f\u3060\u3057, \u6700\u5f8c\u306e\u30d6\u30ed\u30c3\u30af\u306e\u9ad8\u3055\u304c\u7b49\u3057\u3044\u3068\u304d\u306f\u305d\u306e\u5024\u3092\u8003\u3048\u308b\u3082\u306e\u3068\u3059\u308b.<\/p><\/li>\r\n<\/ol>\r\n

        \r\n\r\n

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

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

          \r\n

        1. 1*<\/strong>\u3000\\(m \\neq n\\) \u306e\u3068\u304d
          \r\n\\(n-m\\) \u56de\u76ee\u3067\u88cf\u304c\u51fa\u3066, \u6b8b\u308a \\(m\\) \u56de\u304c\u3059\u3079\u3066\u8868\u3067\u3042\u308b\u5834\u5408\u306a\u306e\u3067\r\n\\[\r\np _ m = (1-p) p^m\r\n\\]<\/li>\r\n

        2. 2*<\/strong>\u3000\\(m=n\\) \u306e\u3068\u304d
          \r\n\\(n\\) \u56de\u304c\u3059\u3079\u3066\u8868\u3067\u3042\u308b\u5834\u5408\u306a\u306e\u3067\r\n\\[\r\np _ n = p^n\r\n\\]<\/li>\r\n<\/ol>\r\n

          \u4ee5\u4e0a\u3088\u308a\r\n\\[\r\np _ m = \\underline{\\left\\{ \\begin{array}{ll} (1-p) p^m & ( m \\neq n \\text{\u306e\u3068\u304d} )\\\\ p^m & ( m=n \\text{\u306e\u3068\u304d} ) \\end{array} \\right.}\r\n\\]\r\n

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

            \r\n

          1. 1*<\/strong>\u3000\\(m \\neq n\\) \u306e\u3068\u304d\r\n\\[\\begin{align}\r\nq _ m & = \\textstyle\\sum\\limits _ {k=0}^{m} p _ k \\\\\r\n& = (1-p) \\cdot \\dfrac{1-p^{m+!}}{1-p} \\\\\r\n& = 1 -p^{m+1}\r\n\\end{align}\\]<\/li>\r\n

          2. 2*<\/strong>\u3000\\(m=n\\) \u306e\u3068\u304d, \u660e\u3089\u304b\u306b\r\n\\[\r\np _ n = 1\r\n\\]<\/li>\r\n<\/ol>\r\n

            \u4ee5\u4e0a\u3088\u308a\r\n\\[\r\np _ m = \\underline{\\left\\{ \\begin{array}{ll} 1 -p^{m+1} & ( m \\neq n \\text{\u306e\u3068\u304d} )\\\\ 1 & ( m=n \\text{\u306e\u3068\u304d} ) \\end{array} \\right.}\r\n\\]\r\n

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

              \r\n

            1. 1*<\/strong>\u3000\\(m=0\\) \u306e\u3068\u304d\r\n\\[\r\nr _ 0 = {p _ 0}^2 = (1-p)^2\r\n\\]<\/li>\r\n

            2. 2*<\/strong>\u3000\\(1 \\leqq m \\leqq n-1\\) \u306e\u3068\u304d\r\n\\[\\begin{align}\r\nr _ m & = {q _ m}^2 -{q _ {m-1}}^2 \\\\\r\n& = \\left( 1-q^{m+1} \\right)^2 -\\left( 1-q^m \\right)^2 \\\\\r\n& = p^m (1-p) \\left\\{ 2-p^m (1+p) \\right\\}\r\n\\end{align}\\]\r\n\u3053\u308c\u306f1*<\/strong>\u306e\u5834\u5408\u3082\u6e80\u305f\u3057\u3066\u3044\u308b.<\/p><\/li>\r\n

            3. 3*<\/strong>\u3000\\(m=n\\) \u306e\u3068\u304d\r\n\\[\\begin{align}\r\nr _ n & = {q _ n}^2 -{q _ {n-1}}^2 \\\\\r\n& = 1 -\\left( 1-p^n \\right)^2 \\\\\r\n& = p^n \\left( 2 -p^n \\right)\r\n\\end{align}\\]<\/li>\r\n<\/ol>\r\n

              \u4ee5\u4e0a\u3088\u308a\r\n\\[\r\np _ m = \\underline{\\left\\{ \\begin{array}{ll} p^m (1-p) \\left\\{ 2-p^m (1+p) \\right\\} & ( m \\neq n \\text{\u306e\u3068\u304d} )\\\\ p^m \\left( 2 -p^m \\right) & ( m=n \\text{\u306e\u3068\u304d} ) \\end{array} \\right.}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\u8868\u304c\u51fa\u308b\u78ba\u7387\u304c \\(p\\) , \u88cf\u304c\u51fa\u308b\u78ba\u7387\u304c \\(1-p\\) \u3067\u3042\u308b\u3088\u3046\u306a\u786c\u8ca8\u304c\u3042\u308b. \u305f\u3060\u3057, \\(0 \\lt p \\lt 1\\) \u3068\u3059\u308b. \u3053\u306e\u786c\u8ca8\u3092\u6295\u3052\u3066, \u6b21\u306e\u30eb\u30fc\u30eb (R) \u306e\u4e0b\u3067, \u30d6\u30ed\u30c3\u30af\u7a4d\u307f\u30b2\u30fc\u30e0\u3092\u884c\u3046 … \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":[105],"tags":[149,109],"class_list":["post-731","post","type-post","status-publish","format-standard","hentry","category-tokyo_b_2007","tag-tokyo_b","tag-109"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/731","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=731"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/731\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=731"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=731"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=731"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}