4. Functions of Random Variables (a) (10 points} Suppose that X is uniformly distributed on the interval [0,1] and Y = ~07. Determine the expression for the probability density function fy (y). You need to show your work to receive full credit. Make sure that your solution is clearly dened for all values of y. (b) (10 points} Suppose the random variables X and Y are statistically independent exponential random variables both with mean values equal to 1. Find the pdf of the random variable Z = X + F. You need to show your work to receive full credit