5. Suppose Z and X are as in Question 4 and that Y is a Bernoulli random variable with success probability 1/2, independent of Z (and hence independent of X). Fact: For independent X and Y, it holds that P(Y ( AnX E B) = P(Y ( A)P(X ( B) for any sets A and B of real numbers. (a) Use the given fact to find an expression for the cumulative distribution function of the random variable W = YX. Hint: For any real number t, P(W