1. Let X and Y be independent continuous random variables that are uniformly distributed on (0, 1). Let H = (X + 2) Y. Find the probability P (In H z) where z is a given number that satisfies e < 2. Your answer should be a function of z. Hint: Condition on X. P (In H2)= 2. Let X be a standard normal random variable, and let Fx (x) be its CDF. Consider the random variable Z = Fx (X). Find the PDF fz (z) of Z. Note that fz (z) takes values in (0, 1). fz (z) =