作者alice90426 (IceSnowSmart)
看板Grad-ProbAsk
標題Re: [商管] [統計]-東吳98-財務工程與精算數學-貝ꐠ…
時間Wed Nov 11 22:31:12 2009
: 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
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參考答案 歡迎討論
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◆ From: 59.120.53.85
1F：推 pushfish:第二小題的作法是假設good driver 但題目好像沒指定~ 11/12 00:30
2F：→ pushfish:是我想錯囉 SORRY~~ 11/12 00:34
3F：→ pushfish:變異數 43/190+4*24/190-(91/190)^2=0.5021 11/12 00:38
4F：推 pushfish:這一題好酷 因為加了條件 讓原本好司機跟壞司機機率變了 11/12 00:42
5F：→ jackoyu:但是題目中的 policyholder 是只 zero claim in one year, 11/12 09:03
6F：→ jackoyu:one claim in year 2, 但題目中的 0.2 不是指 one year 11/12 09:05
7F：→ jackoyu:所以是直接用0.2就可以嗎? 11/12 09:06
※ 編輯: alice90426 來自: 140.114.32.87 (11/12 13:11)