Re: [商管] [統計]-東吳98-財務工程與精算數學-貝ꐠ…

看板Grad-ProbAsk作者alice90426 (IceSnowSmart)時間16年前 (2009/11/11 22:31)推噓2(2推 0噓 5→)

留言7則, 2人參與討論串2/2 (看更多)

: 1. : There are two types of driver. Good driver makes 75% of the population and : in one year have zero claims with probability 0.7, one claim with probability : 0.2, and two claims with probability 0.1. Bad drivers makes up 25% of the : population and have zero, one, or two claims with probability 0.5, 0.3, 0.2, : respectively. For a particular policyholder, suppose we have observed zero : claim in year 1 and one claim in year 2. : 1) What is the probability that the policyholder is a good driver? Pr(所求)=0.75*0.7*0.2/[0.75*0.7*0.2+0.25*0.5*0.3] =14/19 : 2) What is the probability that the policyholder makes no claims next year? Pr(所求)=14/19*0.7+5/19*0.5=123/190 : 3) What is the expected number of claims next year? What is the Variance? Pr(0 claim)=123/190 Pr(1 claim)=14/19*0.2+5/19*0.3=43/190 Pr(2 claim)=14/19*0.1+5/19*0.2=24/190=12/95 E(X)=[43/190]*1+[12/95]*2=91/190 Var(X)=123/190*[91/190]^2+43/190*[99/190]^2+12/95*[289/190]^2=0.5021 訂正了變異數第一次算沒算到0 claim的 -- 參考答案歡迎討論 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 59.120.53.85

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