{"id":1204,"date":"2015-07-29T23:06:05","date_gmt":"2015-07-29T14:06:05","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=1204"},"modified":"2021-10-30T20:12:45","modified_gmt":"2021-10-30T11:12:45","slug":"tkb201402","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tkb201402\/","title":{"rendered":"\u6771\u5927\u6587\u7cfb2014\uff1a\u7b2c2\u554f"},"content":{"rendered":"<hr \/>\n<p>\\(a\\) \u3092\u81ea\u7136\u6570\uff08\u3059\u306a\u308f\u3061 \\(1\\) \u4ee5\u4e0a\u306e\u6574\u6570\uff09\u306e\u5b9a\u6570\u3068\u3059\u308b.\r\n\u767d\u7403\u3068\u8d64\u7403\u304c\u3042\u308f\u305b\u3066 \\(1\\) \u500b\u4ee5\u4e0a\u5165\u3063\u3066\u3044\u308b\u888b U \u306b\u5bfe\u3057\u3066, \u6b21\u306e\u64cd\u4f5c <strong>(\uff0a)<\/strong> \u3092\u8003\u3048\u308b.<\/p>\r\n<ol>\r\n<li><p><strong>(\uff0a)<\/strong>\u3000\u888b U \u304b\u3089\u7403\u3092 \\(1\\) \u500b\u53d6\u308a\u51fa\u3057,\r\n<ol>\r\n<li><p><strong>(i)<\/strong>\u3000\u53d6\u308a\u51fa\u3057\u305f\u7403\u304c\u767d\u7403\u306e\u3068\u304d\u306f, \u888b U \u306e\u4e2d\u8eab\u304c\u767d\u7403 \\(a\\) \u500b, \u8d64\u7403 \\(1\\) \u500b\u3068\u306a\u308b\u3088\u3046\u306b\u3059\u308b.<\/p><\/li>\r\n<li><p><strong>(ii)<\/strong>\u3000\u53d6\u308a\u51fa\u3057\u305f\u7403\u304c\u8d64\u7403\u306e\u3068\u304d\u306f, \u305d\u306e\u7403\u3092\u888b U \u3078\u623b\u3059\u3053\u3068\u306a\u304f, \u888b U \u306e\u4e2d\u8eab\u306f\u305d\u306e\u307e\u307e\u306b\u3059\u308b.<\/p><\/li>\r\n<\/ol><\/p><\/li>\r\n<\/ol>\r\n<p>\u306f\u3058\u3081\u306b\u888b U \u306e\u4e2d\u306b, \u767d\u7403\u304c \\(a+2\\) \u500b, \u8d64\u7403\u304c \\(1\\) \u500b\u5165\u3063\u3066\u3044\u308b\u3068\u3059\u308b. \u3053\u306e\u888b U \u306b\u5bfe\u3057\u3066\u64cd\u4f5c <strong>(\uff0a)<\/strong> \u3092\u7e70\u308a\u8fd4\u3057\u884c\u3046.\r\n\u305f\u3068\u3048\u3070, \\(1\\) \u56de\u76ee\u306e\u64cd\u4f5c\u3067\u767d\u7403\u304c\u51fa\u305f\u3068\u3059\u308b\u3068, \u888b U \u306e\u4e2d\u8eab\u306f\u767d\u7403 \\(a\\) \u500b, \u8d64\u7403 \\(1\\) \u500b\u3068\u306a\u308a, \u3055\u3089\u306b \\(2\\) \u56de\u76ee\u306e\u64cd\u4f5c\u3067\u8d64\u7403\u304c\u51fa\u305f\u3068\u3059\u308b\u3068, \u888b U \u306e\u4e2d\u8eab\u306f\u767d\u7403 \\(a\\) \u500b\u306e\u307f\u3068\u306a\u308b.\r\n\\(n\\) \u56de\u76ee\u306b\u53d6\u308a\u51fa\u3057\u305f\u7403\u304c\u8d64\u7403\u3067\u3042\u308b\u78ba\u7387\u3092 \\(p _ n\\) \u3068\u3059\u308b. \u305f\u3060\u3057, \u888b U \u306e\u4e2d\u306e\u500b\u3005\u306e\u7403\u306e\u53d6\u308a\u51fa\u3055\u308c\u308b\u78ba\u7387\u306f\u7b49\u3057\u3044\u3082\u306e\u3068\u3059\u308b.<\/p>\r\n<ol>\r\n<li><p><strong>(1)<\/strong>\u3000\\(p _ 1\\) , \\(p _ 2\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<li><p><strong>(2)<\/strong>\u3000\\(n \\geqq 3\\) \u306b\u5bfe\u3057\u3066 \\(p _ n\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n<hr \/>\r\n<!--more-->\r\n<h4>\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n<p><strong>(1)<\/strong><\/p>\r\n<p>\\(p _ 1\\) \u306b\u3064\u3044\u3066, \u64cd\u4f5c\u524d\u306e\u72b6\u614b\u304b\u3089\r\n\\[\r\np _ 1 = \\underline{\\dfrac{1}{a+3}}\r\n\\]\r\n\\(p _ 2\\) \u306b\u3064\u3044\u3066, \\(1\\) \u56de\u76ee\u306b\u51fa\u305f\u7403\u306e\u8272\u306b\u3088\u3063\u3066\u5834\u5408\u5206\u3051\u3057\u3066\u8003\u3048\u308b.<\/p>\r\n<ol>\r\n<li><p><strong>1*<\/strong>\u3000\\(1\\) \u56de\u76ee\u304c\u8d64\u7403\u306e\u3068\u304d<br \/>\r\n\u888b\u306e\u4e2d\u306b\u306f, \u767d\u7403 \\(a+2\\) \u500b\u306e\u307f\u3067\u3042\u308b.<\/p><\/li>\r\n<li><p><strong>2*<\/strong>\u3000\\(1\\) \u56de\u76ee\u304c\u767d\u7403\u306e\u3068\u304d<br \/>\r\n\u888b\u306e\u4e2d\u306b\u306f, \u767d\u7403 \\(a\\) \u500b\u3068\u8d64\u7403 \\(1\\) \u500b\u304c\u5165\u3063\u3066\u3044\u308b.<\/p><\/li>\r\n<\/ol>\r\n<p>\u3057\u305f\u304c\u3063\u3066\r\n\\[\\begin{align}\r\np _ 2 & = p _ 1 \\cdot 0 +( 1 - p _ 1 ) \\cdot \\dfrac{1}{a+1} \\\\\r\n& = \\underline{\\dfrac{a+2}{(a+3)(a+1)}}\r\n\\end{align}\\]\r\n<p><strong>(2)<\/strong><\/p>\r\n<p>\\(n\\ \\ ( n \\geqq 1 )\\) \u56de\u64cd\u4f5c\u3092\u884c\u3063\u305f\u5f8c\u306e\u888b\u306e\u4e2d\u306e\u72b6\u614b\u306f, \\(n\\) \u56de\u76ee\u306b\u51fa\u305f\u7403\u306e\u8272\u306b\u5fdc\u3058\u305f \\(2\\) \u3064\u306e\u72b6\u614b\u3057\u304b\u306a\u3044.<\/p>\r\n<ul>\r\n<li><p>\u767d\u7403\u304c\u51fa\u305f\u5f8c\u3067, \u767d\u7403 \\(a\\) \u500b, \u8d64\u7403 \\(1\\) \u500b\u304c\u5165\u3063\u3066\u3044\u308b.<\/p><\/li>\r\n<li><p>\u8d64\u7403\u304c\u51fa\u305f\u5f8c\u3067, \u767d\u7403\u3057\u304b\u306a\u3044.<\/p><\/li>\r\n<\/ul>\r\n<p>\u306a\u306e\u3067, \\(p _ {n+1}\\) \u306f \\(p _ n\\) \u3092\u7528\u3044\u3066\r\n\\[\\begin{align}\r\np _ {n+1} & = p _ n \\cdot 0 + ( 1 - p _ n ) \\cdot \\dfrac{1}{a+1} \\\\\r\n& = \\dfrac{1 - p _ n}{a+1}\r\n\\end{align}\\]\r\n\u3053\u308c\u3092\u5909\u5f62\u3059\u308b\u3068\r\n\\[\r\np _ {n+1} -\\dfrac{1}{a+2} = -\\dfrac{1}{a+1} \\left( p _ n -\\dfrac{1}{a+2} \\right)\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066, \u6570\u5217 \\(\\left\\{ p _ n -\\dfrac{1}{a+2} \\right\\}\\) \u306f, \u521d\u9805 \\(p _ 1 -\\dfrac{1}{a+2}\\) , \u516c\u6bd4 \\(-\\dfrac{1}{a+1}\\) \u306e\u7b49\u6bd4\u6570\u5217\u3068\u306a\u308b.\r\n\\[\\begin{align}\r\np _ n -\\dfrac{1}{a+2} & = \\left( \\dfrac{1}{a+3} -\\dfrac{1}{a+2} \\right) \\left( -\\dfrac{1}{a+1} \\right)^{n-1} \\\\\r\n\\text{\u2234} \\quad p _ n & = \\underline{\\dfrac{1}{a+2} \\left\\{ 1 -\\dfrac{1}{a+3} \\left( -\\dfrac{1}{a+1} \\right)^{n-1} \\right\\}}\r\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"\\(a\\) \u3092\u81ea\u7136\u6570\uff08\u3059\u306a\u308f\u3061 \\(1\\) \u4ee5\u4e0a\u306e\u6574\u6570\uff09\u306e\u5b9a\u6570\u3068\u3059\u308b. \u767d\u7403\u3068\u8d64\u7403\u304c\u3042\u308f\u305b\u3066 \\(1\\) \u500b\u4ee5\u4e0a\u5165\u3063\u3066\u3044\u308b\u888b U \u306b\u5bfe\u3057\u3066, \u6b21\u306e\u64cd\u4f5c (\uff0a) \u3092\u8003\u3048\u308b. (\uff0a)\u3000\u888b U \u304b\u3089\u7403\u3092 \\(1\\) \u500b\u53d6\u308a\u51fa\u3057 &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/tkb201402\/\">\u7d9a\u304d\u3092\u8aad\u3080 <span class=\"meta-nav\">&rarr;<\/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":[123],"tags":[149,112],"class_list":["post-1204","post","type-post","status-publish","format-standard","hentry","category-tokyo_b_2014","tag-tokyo_b","tag-112"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1204","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=1204"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1204\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1204"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1204"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1204"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}