Three fair coins are flipped simultaneously. All the coins that come up tails are flipped once more. Let X denote the number of coins that come up heads on the first toss, and let Y represent the number of re-tossed coins that come up heads on the second flipping. (a) 0.5 pt - Find the admissible values for X, and find the possible values that Y can take conditioned on X. (b) 0.5 pt - Find the marginal PMF and the mean of X. (c) 1 pt - Find the joint PMF of X and Y. (d) 1 pt - Calculate the expected value of X+Y (possibly using indicator functions). (e) 1 pt - Derive a formula for E[Y|X] and use it to compute E[E[X +Y|X]]. (f) 1 pt - Find the PMF of U = X+Y and compute E[U].