7. [15 points] Let N be drawn from the Poisson(1) distribution, and let X1, ..., XN be i.i.d. random variables drawn from the Uniform[0, 1] distribution. Define the random variable S = X1 + . .. + XN, so that S = 0 if N = 0. Recall that a Poisson(A) random variable has mean > and variance 1. (a) [5 points] Compute E[S] and Var(S). (b) [5 points] Compute Cov(S, N). 6 (c) [5 points] Approximate the probability P(S > 620 | N = 1200)