Answer Happy

7. Given the value of a, claim frequency has the probability mass function 3* e-3 PX = a +(1-a) k=0, 1, 2, ... k! k! and the conditionally independent across the year. The parameter a varies by individual, and has a prior density function na) = 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!n! H(m,n) = ['*"(1-x)"dx (m+n+1)! for m, n being non-negative integers.] 0