Problem 3: (15 points) Let X be a uniform random variable on [0,1] and let Y be a uniform random variable on [0,2]. Then the probability density functions of X and Y are fx (x ) = 1 Ox=1 otherwise' fr (x) = $1/2 05x52 otherwise Suppose X and Y are independent random variables. Determine the probability density function fx+r(x) for X + Y. Problem 4: (15 points) Let X be a uniform random variable on [0,1] and let Y be an exponential random variable with parameter ) = 1. Then the probability density functions of X and Y are fx (x ) = 10 otherwise' fr (xx ) = 1 x