Problem 1. You are given the following information about N, the annual number of claims for a randomly selected insured: P(N= 0)= P(N = 1) = 2' = 3' 1 6' P(N > 1)= Let S denote the total annual claim amount for an insured. When N = 1, S is exponentially distributed with mean 5. When N > 1, S is exponentially distributed with mean 8. (a) Determine P(4 <S <8). (b) Determine E(S).