{"id":2034,"date":"2021-12-15T00:13:00","date_gmt":"2021-12-14T15:13:00","guid":{"rendered":"https:\/\/www.roundown.net\/nyushi\/?p=2034"},"modified":"2021-12-15T00:13:00","modified_gmt":"2021-12-14T15:13:00","slug":"wsr202104","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/wsr202104\/","title":{"rendered":"\u65e9\u7a32\u7530\u7406\u5de52021\uff1a\u7b2c4\u554f"},"content":{"rendered":"
\n

\\(n , k\\) \u3092 \\(2\\) \u4ee5\u4e0a\u306e\u81ea\u7136\u6570\u3068\u3059\u308b.\r\n\\(n\\) \u500b\u306e\u7bb1\u306e\u4e2d\u306b \\(k\\) \u500b\u306e\u7389\u3092\u7121\u4f5c\u70ba\u306b\u5165\u308c, \u5404\u7bb1\u306b\u5165\u3063\u305f\u7389\u306e\u500b\u6570\u3092\u6570\u3048\u308b.\r\n\u305d\u306e\u6700\u5927\u5024\u3068\u6700\u5c0f\u5024\u306e\u5dee\u304c \\(\\ell\\) \u3068\u306a\u308b\u78ba\u7387\u3092 \\(P _ {\\ell} \\ ( 0 \\leqq \\ell \\leqq k )\\) \u3068\u3059\u308b.\r\n\u3053\u306e\u3068\u304d, \u4ee5\u4e0b\u306e\u554f\u306b\u7b54\u3048\u3088.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(n = 2\\) , \\(k = 3\\) \u306e\u3068\u304d, \\(P_0 , P_1 , P_2 , P_3\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(n \\geqq 2\\) , \\(k = 2\\) \u306e\u3068\u304d, \\(P_0 , P_1 , P_2\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000\\(n \\geqq 3\\) , \\(k = 3\\) \u306e\u3068\u304d, \\(P_0 , P_1 , P_2 , P_3\\) \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

    \u7389\u306e\u5165\u308c\u65b9\u306f, \\(2^3 = 8\\) \u901a\u308a.
    \r\n\\(\\ell = 0 , 2\\) \u306b\u306f\u306a\u3089\u306a\u3044\u306e\u3067\r\n\\[\r\nP_0 = P_2 = 0\r\n\\]\r\n\\(\\ell = 3\\) \u306b\u306a\u308b\u306e\u306f, \u7389\u3092\u5165\u308c\u308b\u7bb1\u306e\u9078\u3073\u65b9\u304c \\(2\\) \u901a\u308a\u3042\u308b\u306e\u3067\r\n\\[\r\nP_3 = \\dfrac{2}{8} = \\dfrac{1}{4}\r\n\\]\r\n\\(\\ell = 1\\) \u306b\u306a\u308b\u306e\u306f, \u4f59\u4e8b\u8c61\u3092\u8003\u3048\u3066\r\n\\[\r\nP_1 = 1 -\\dfrac{1}{4} = \\dfrac{3}{4}\r\n\\]\r\n\u4ee5\u4e0a\u3088\u308a\r\n\\[\r\nP_0 = \\underline{0} \\ , \\ P_1 = \\underline{\\dfrac{3}{4}} \\ , \\ P_2 = \\underline{0} \\ , \\ P_3 = \\underline{\\dfrac{1}{4}}\r\n\\]\r\n

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

      \r\n

    1. 1*<\/strong>\u3000\\(n = 2\\) \u306e\u3068\u304d
      \r\n\u7389\u306e\u5165\u308c\u65b9\u306f \\(2^2 = 4\\) \u901a\u308a.
      \r\n\\(\\ell = 1\\) \u306b\u306f\u306a\u3089\u306a\u3044\u306e\u3067\r\n\\[\r\nP_1 = 0\r\n\\]\r\n\\(\\ell = 2\\) \u306b\u306a\u308b\u306e\u306f, \u7389\u3092\u5165\u308c\u308b\u7bb1\u306e\u9078\u3073\u65b9\u304c \\(2\\) \u901a\u308a\u3042\u308b\u306e\u3067\r\n\\[\r\nP_2 \uff1d\\dfrac{2}{4} = \\dfrac{1}{2}\r\n\\]\r\n\\(\\ell = 0\\) \u306b\u306a\u308b\u306e\u306f, \u4f59\u4e8b\u8c61\u3092\u8003\u3048\u3066\r\n\\[\r\nP_1 = 1 -\\dfrac{1}{2} = \\dfrac{1}{2}\r\n\\]<\/li>\r\n

    2. 2*<\/strong>\u3000\\(n \\geqq 3\\) \u306e\u3068\u304d
      \r\n\u7389\u306e\u5165\u308c\u65b9\u306f \\(n^2\\) \u901a\u308a.
      \r\n\\(\\ell = 0\\) \u306b\u306f\u306a\u3089\u306a\u3044\u306e\u3067\r\n\\[\r\nP_0 = 0\r\n\\]\r\n\\(\\ell = 2\\) \u306b\u306a\u308b\u306e\u306f, \u7389\u3092\u5165\u308c\u308b\u7bb1\u306e\u9078\u3073\u65b9\u304c \\(n\\) \u901a\u308a\u3042\u308b\u306e\u3067\r\n\\[\r\nP_2 \uff1d\\dfrac{n}{n^2} = \\dfrac{1}{n}\r\n\\]\r\n\\(\\ell = 1\\) \u306b\u306a\u308b\u306e\u306f, \u4f59\u4e8b\u8c61\u3092\u8003\u3048\u3066\r\n\\[\r\nP_1 = 1 -\\dfrac{1}{n} = \\dfrac{n-1}{n}\r\n\\]<\/li>\r\n<\/ol>\r\n

      \u4ee5\u4e0a\u3088\u308a, \u6c42\u3081\u308b\u78ba\u7387\u306f\r\n\\[\r\n\\underline{\\left\\{ \\begin{array}{ll} P_0 = \\dfrac{1}{2} \\ , \\ P_1 = 0 \\ , \\ P_2 = \\dfrac{1}{2} & ( \\ n = 2 \\ \\text{\u306e\u3068\u304d} \\ ) \\\\ P_0 = 0 \\ , \\ P_1 = \\dfrac{n-1}{n} \\ , \\ P_2 = \\dfrac{1}{n} & ( \\ n \\geqq 3 \\ \\text{\u306e\u3068\u304d} \\ ) \\end{array} \\right.}\r\n\\]\r\n

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

        \r\n

      1. 1*<\/strong>\u3000\\(n = 3\\) \u306e\u3068\u304d
        \r\n\u7389\u306e\u5165\u308c\u65b9\u306f \\(3^3 = 27\\) \u901a\u308a.
        \r\n\\(\\ell = 1\\) \u306b\u306f\u306a\u3089\u306a\u3044\u306e\u3067\r\n\\[\r\nP_1 = 0\r\n\\]\r\n\\(\\ell = 0\\) \u306b\u306a\u308b\u306e\u306f, \\(3\\) \u500b\u306e\u7bb1\u306b \\(1\\) \u3064\u305a\u3064\u7389\u3092\u5165\u308c\u308b\u65b9\u6cd5\u306f \\(3 ! = 6\\) \u901a\u308a\u3042\u308b\u306e\u3067\r\n\\[\r\nP_0 = \\dfrac{6}{27} = \\dfrac{2}{9}\r\n\\]\r\n\\(\\ell = 3\\) \u306b\u306a\u308b\u306e\u306f, \u7389\u3092\u5165\u308c\u308b\u7bb1\u306e\u9078\u3073\u65b9\u304c \\(3\\) \u901a\u308a\u3042\u308b\u306e\u3067\r\n\\[\r\nP_3 = \\dfrac{3}{27} = \\dfrac{1}{9}\r\n\\]\r\n\\(\\ell = 2\\) \u306b\u306a\u308b\u306e\u306f, \u4f59\u4e8b\u8c61\u3092\u8003\u3048\u3066\r\n\\[\r\nP_2 = 1 -\\dfrac{2}{9} -\\dfrac{1}{9} = \\dfrac{2}{3}\r\n\\]<\/li>\r\n

      2. 2*<\/strong>\u3000\\(n \\geqq 4\\) \u306e\u3068\u304d
        \r\n\u7389\u306e\u5165\u308c\u65b9\u306f \\(n^3\\) \u901a\u308a.
        \r\n\\(\\ell = 0\\) \u306b\u306f\u306a\u3089\u306a\u3044\u306e\u3067\r\n\\[\r\nP_0 = 0\r\n\\]\r\n\\(\\ell = 3\\) \u306b\u306a\u308b\u306e\u306f, \u7389\u3092\u5165\u308c\u308b\u7bb1\u306e\u9078\u3073\u65b9\u304c \\(n\\) \u901a\u308a\u3042\u308b\u306e\u3067\r\n\\[\r\nP_3 = \\dfrac{n}{n^3} = \\dfrac{1}{n^2}\r\n\\]\r\n\\(\\ell = 1\\) \u306b\u306a\u308b\u306e\u306f, \\(n\\) \u500b\u306e\u7bb1\u306e\u3046\u3061 \\(3\\) \u500b\u306e\u7bb1\u306b \\(1\\) \u3064\u305a\u3064\u7389\u3092\u5165\u308c\u308b\u65b9\u6cd5\u306f \\({} _ {n} \\text{P}{} _ {3} = n (n-1) (n-2)\\) \u901a\u308a\u3042\u308b\u306e\u3067\r\n\\[\r\nP_1 = \\dfrac{n (n-1) (n-2)}{n^3} = \\dfrac{(n-1) (n-2)}{n^2}\r\n\\]\r\n\\(\\ell = 2\\) \u306b\u306a\u308b\u306e\u306f, \u4f59\u4e8b\u8c61\u3092\u8003\u3048\u3066\r\n\\[\r\nP_2 = 1 -\\dfrac{1}{n^2} -\\dfrac{(n-1) (n-2)}{n^2} = \\dfrac{3 (n-1)}{n^2}\r\n\\]<\/li>\r\n<\/ol>\r\n

        \u4ee5\u4e0a\u3088\u308a, \u6c42\u3081\u308b\u78ba\u7387\u306f\r\n\\[\r\n\\underline{\\left\\{ \\begin{array}{ll} P_0 = \\dfrac{2}{9} \\ , \\ P_1 = 0 \\ , \\ P_2 = \\dfrac{2}{3} \\ , \\ P_3 = \\dfrac{1}{9} & ( \\ n = 3 \\ \\text{\u306e\u3068\u304d} \\ ) \\\\ P_0 = 0 \\ , \\ P_1 = \\dfrac{(n-1) (n-2)}{n^2} \\ , \\ P_2 = \\dfrac{3 (n-1)}{n^2} \\ , \\ P_3 = \\dfrac{1}{n^2} & ( \\ n \\geqq 4 \\ \\text{\u306e\u3068\u304d} \\ ) \\end{array} \\right.}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(n , k\\) \u3092 \\(2\\) \u4ee5\u4e0a\u306e\u81ea\u7136\u6570\u3068\u3059\u308b. \\(n\\) \u500b\u306e\u7bb1\u306e\u4e2d\u306b \\(k\\) \u500b\u306e\u7389\u3092\u7121\u4f5c\u70ba\u306b\u5165\u308c, \u5404\u7bb1\u306b\u5165\u3063\u305f\u7389\u306e\u500b\u6570\u3092\u6570\u3048\u308b. \u305d\u306e\u6700\u5927\u5024\u3068\u6700\u5c0f\u5024\u306e\u5dee\u304c \\(\\ell\\) \u3068\u306a\u308b\u78ba\u7387\u3092 \\(P _ … \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":[177],"tags":[147,165],"class_list":["post-2034","post","type-post","status-publish","format-standard","hentry","category-waseda_r_2021","tag-waseda_r","tag-165"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/2034","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=2034"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/2034\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=2034"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=2034"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=2034"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}