[問題] 請教一個機率問題

看板CFAiafeFSA (精算師/基金經理人/銀行家)作者linki (111111)時間17年前 (2008/09/04 15:25)推噓0(0推 0噓 2→)

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這是actex study manual module 3 poisson process的example 3.20 根據3.19的題意延伸 p(wating time of the claim from Texas < wating time of the claim from Missouri)=0.6 也就是claim from Texas會比Missouri早發生的機率為0.6 而3.20問到 For the insurance company in the preceding example: (a) Find the probablity that three claims from Texas are received before the first claim from Missouri. (b) Find the probablity that three claims from Texas are received before the third claim from Missouri. (a)是比較沒問題，就是發生的前三件事都是from Texas 所以答案是0.6x0.6x0.6=0.216 (b)我解讀題意是在第三次的案件來自Missouri前，發生三次案件來自Texas 不知道有沒有解讀錯(不好意思，小弟英文不是很好) 我的想法是用負二項分配來解題，也就是把claim from Missouri當成功(p=0.4) 也就是利用負二項分配計算在第三次成功前，有三次失敗的機率 c5取3x0.4^3x0.6^3=0.13824 但解答出來卻不是如此想請教各位大大是我對題目解讀錯誤還是觀念錯了謝謝各位附上(b)之解答 Consider the first five claims received. Three claims from Texas will be received before the third claim from Missouri if and only if three or more of the first five claims come from Texas. The number of claims from Texas in the first five claims received follows a binomial distribution with n=5 and p=0.6 The probability that three or more of the first 5claims came from Texas is p(3)+p(4)+p(5)=0.6826 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 61.228.147.52