Help needed and thanks in advance !!

(a) (20 marks) Suppose that N SN = XitX2 + . . . +XN = >Xi, 1=1 where {Xi, i = 1, ..., N} are independent and identically distributed ran- dom variables and / is a non-negative random variable independent of X;s. Let u and o' be the mean and variance of X,s, respectively (i.e. E(X,) = p and V(X,) = o' for all i = 1, ..., N). Find E(SN) and V(SN). [Hint: Use the fact that E(SN) = E[E(SN|N)] and V(SN) = E[V(SN|N)] + VIE(SNIN)]] (b) (20 marks) Suppose that a company has determined that the number of jobs per week, N, varies from week to week and has a Poisson distribution with mean A. The number of hours to complete each job, Y, is gamma distributed with parameters o and 8. The total time to complete all jobs in a week is T = _MY;. Find the expected value and the variance of the total time to complete all jobs