In: Statistics and Probability
In this problem there are two random variables X and Y. The random variable Y counts how many times we roll the die in the following experiment: First, we flip a fair coin. If it comes Heads we set X= 1 and roll a fair die until we get a six. If it comes Tails, we set X= 0 and roll the die until we get an even number (2, 4 or 6).
a). What are the possible values taken by the pair (X,Y)? What is the probability that (X,Y) =(0,k) fork= 1,2,...? What is the join mass distribution function of the pair (X,Y)?
b). What is the mass distribution of the second marginal of (X,Y), that is, the mass distribution of Y?