Let x be a fair dice roll, that is a sample from the uniform distribution in f1; 2; : : : ; 6g. let y be the number of heads in x tosses of a fair coin, that is a coin which is landing heads with probability 1 2 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 jx = x) for any x = 1; 2; : : : ; 6. b. prove that e(y ) = 1 2 e(x) (1) and derive the value of e(y ). explain intuitively why (1) makes sense.