I 34-3 P = a k! 7. Given the value of a, claim frequency has the probability mass function e - +(1-a) k=0, 1, 2, ... k!

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I 34 3 P A K 7 Given The Value Of A Claim Frequency Has The Probability Mass Function E 1 A K 0 1 2 K 1 (36.4 KiB) Viewed 25 times

I 34-3 P = a k! 7. Given the value of a, claim frequency has the probability mass function e - +(1-a) k=0, 1, 2, ... k! and the conditionally independent across the year. The parameter a varies by individual, and has a prior density function (a) = 2(1 - a), 0<a< 1. For an individual, there is one claim in year 1 and 2 claims in year 2. (a) Determine the posterior distribution of a for the individual. (b) Find the posterior mean of a for the individual. (c) Hence, find the expected number of claims in year 3 for the individual. [Note: You can use the following result for Euler integral of the first kind: m!! (m+n+1)! for n being non-negative integers.] H(m,n) = ['>"(1-x)"dx=; m,