Coins and dice. let x be a fair dice roll, that is a sample from the uniform distribution in {1, 2, }. let y be the number of heads in x tosses of a fair coin, that is a coin which is landing heads with probability and tails otherwise. we assume the outcome of each coin toss is independent from the outcome of the other coin tosses and from x. a. compute e (y|x = x) for any x = 1,2, . b. prove that e(y) = e(x) and derive the value of e (y). explain intuitively why (1) makes sense.