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5. (20 points) Play the following game: Roll two fair six-sided dice. Let X be the sum of the two faces of the dice. Then flip X fair two-sided coins and let Y be the total number of coins that land on heads. (a) For k = 2, 3, 4, ..., 12 calculate E(Y X = k). Show all of your work and explain each step. You may represent your answer as a function of & or as a list. (b) Calculate the unconditioned expectation E(Y). Show all of your work and explain each step