Problem 1. Let A be a random variable that takes values in the positive integers 1, 2, .... Given that NV = n, toss a fair coin n times, and let X be the number of Heads and Y = N - X the number of Tails. What is the covariance of X and Y if (a) N has the Poisson distribution with parameter A > 0? (b) N has the geometric distribution P(N = k) = (1-r)? Please simplify your answers as much as possible