An insurance company sells three types of policies with the following characteristics: Type of Policy Proportion of Total Policies Annual Claim Frequency A B C 5% 20% 75% Poisson with = 0.25 Poisson with = 0.5 Poisson with = 1.00 A randomly selected policyholder is observed to have one claim for the first year and 0 claim for the second year. (a) Find the posterior distribution, i.e. probability to belong to each category after observing claims for the first two years. (b) Determine the Bayesian estimate of the expected number of claims in Year 3.