A car insurance company has a particular policy: Denote N as the number of claims per annum and we assume that N follows a Poisson distribution with parameter /. Claim amounts (X1, Xn) are assumed to be independent from each other; with exponential distribution Ae AT Let S = Xi X; denote the aggregate annual claims from this policy: A check is made for ruin only at the end of the year: Suppose that the premium income per year is (a) Derive the moment generating function of N, Xi and S. [9 marks] (b) Suppose that we can obtain the estimates for the mean and variance of S and denote them as m1 and m2, respectively. If we use a normal approximation to the distribution of S, briefly explain how to calculate the initial capital, U, required in order that the probability of ruin at the end of the first year is 0.01. [3 marks]