1. Consider a two-stage random experiment where you roll a fair, 6-sided die and then you (independently) flip a fair coin as many times as are shown on the die. Define the RV N to be the number you roll on the die, and the RV X to be the total number of heads in the #N subsequent coin flips. (a) (2 points) What is the conditional distribution of X, given that you rolled N = 4? You can give the PMF or, if it is a known distribution, just its name and parameter values. (b) (5 points) Find the joint PMF of (N, X); you can express it is a formula, or a (bivariate) table of probabilities (one for each combination of (N,X) values). (c) (3 points) Find the marginal PMF of X.