Let Z = (Z1, Z2, ...) be an infinite sequence of IID Bernoulli random variables (coin-flips) with P(Zi = 1) = p; P(Zi = 0) = (1 -p). Let W be a Poisson random variable that is independent of Z with mean > > 0. Let X = Z1 + ... + Zw be the total number of ones in W coin-flips and Y = W - X the total number of zeros in W coin flips. Note: X is the sum of a random number of IID coin-flips. Evaluate: . 3 POINTS The joint pmf of X and Y px,y (x, y) . 3 POINTS The marginal pmf of X: Px (x). . 3 POINTS The marginal pmf of Y: py (y). . 3 POINTS Are X and Y orthogonal? Are they independent? Explain