[機統] 期望值 - 中正電機所消失

看板Math作者martine318時間9年前 (2017/01/01 23:01)推噓0(0推 0噓 3→)

留言3則, 2人參與討論串1/3 (看更多)

題目 : Independent trials , each of which is a success with probability p , are performed until there are 3 consecutive successes. What is the mean number of necessary trials. 解答 : 令Nk為連續k次成功所須試驗的平均次數以下Nk、Nk-1、No的k、k-1、o 均為N的下標 Nk = Nk-1 + 1 + (1-p)Nk 且 No = 0 故 N1 = No + 1 + (1-p)N1 => N1 = 1/p 故 N2 = N1 + 1 + (1-p)N2 => N2 = (1/p) + (1/p^2) 故 N3 = N2 + 1 + (1-p)N2 => N3 = (1/p) + (1/p^2) + (1/p^3) ------------------------------------------------------------------------- 想請問一下 Nk = Nk-1 + 1 + (1-p)Nk 這一項怎麼來的呢感謝!! -- ※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 122.117.20.24 ※ 文章網址: https://www.ptt.cc/bbs/Math/M.1483282914.A.299.html

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OppOops

01/01 23:49, , 1^F

01/01 23:49, 1^F

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OppOops

01/01 23:54, , 2^F

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martine318

01/02 00:14, , 3^F

01/02 00:14, 3^F