QUESTION 2 (6 marks) Let N represent the number of accidents arising from a portfolio of risks. Some of these accidents result in claims. Let Mk represent the number of claims for the kth accident. The total number of claims is therefore: 5' = M1 + M2 + + M N, where N = 0 implies that S = 0. Suppose that we have two portfolios where the number of accidents in each portfolio follows a Poisson distribution with parameters A1 = 15 and A2 = 35 respectively. For portfolio 1, the number of claims arising from each accident has the following distribution: Pr(1 claim) = 0.20, Pr(2 claims) = 0.65, Pr(3 claims) = 0.15 For portfolio 2, the number of claims arising from each accident has the following distribution: P'r'(2 claims) = 0.10, Pr(3 claims) = 0.75, Pr(4 claims) = 0.15 (a) Find the distribution of S = 5'1 + 5'2 assuming the risks are independent. (3 marks) (b) Find E(S), Var(S) and the MGF of S