4 A fair die is rolled. Let Y be the face value show ing, 1, 2, 3, 4,5, or 6 with each having the probability of occurring, Let X be another random variable, gíven by SY if Y is even X= {0 if Y is odd. 4a) Find ECY), 44) what is the probability distribution for X? Find ECX). 4c) Find the conditional probabily distribution of Y given each X, 4d) Find the conditional expected value of Y given each value of X, ECY|X). 4e) Find Hhe probability distribution of Z=XY. (Hint: (x3) = {, (x, y) (joint paf)

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