Problem 2. (6 points) Sally has a weighted coin that lands on heads with probability q (and thus lands on tails with probability 1 - q). Suppose Sally performs an experiment where she flips the coin until it lands on heads twice (not necessarily consecutively). Let X be the number of times Sally flips tails before the first head. Let Y be the number of times she flips tails after the first head. For example, if Sally flips TTHTTTTTH, then X = 2 and Y = 5. 1. Write an explicit formula for the joint mass function of X and Y. 2. Compute the marginal probability P(X = i) = _ p(i, j). You may use the geometric series formula Ck- 10 ak = for |x|