A coin is flipped until at least a head and a tail occur. Define two random variables X and Y to be the trial numbers at which the first head and the first tail occur. Assume that at any trial, the probability that a head occurs is pe (0, 1). (a) Find the joint probability P(X = m, Y = n). (b) Verify that your answer in (a) is valid by checking EP(X = m, Y = n) = 1