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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 km accident. The total number of claims is therefore: 5' = M1 + M2 + + MN, 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: Par-(1 claim) = 0.201 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: Pr(2 claims} = 0.10, Pr(3 claims] = {1.75, PT(4 claims) = 0.15 (a) Find the distribution of S = 31 + 3;; assuming the risks are independent. (3 marks) (b) Find 151(3), Var(.5') and the MGF of S