Problem 3 A gambling game operates as follows. A player pays $5 to play. A fair coin is then ipped. If the coin lands heads, then a fair die is rolled. If the coin lands tails, then a loaded die is rolled. The loaded die is such that 13(1): P(2) : 0.3 and [3(3) 13(4) P(5) P(6) 0.1 The player is then paid $2 multiplied by the value appearing on the die. Let X _ 0 if the coin lands heads # 1 if the coin lands tails Let Y denote the value appearing on the die after a roll. 1. Construct the joint PMF of X and Y. P Determine the marginal PMFs of X and Y. 3. What is the expected value of the player's winnings? What is the covariance of X and Y? 5"? What is the correlation between X and Y