Problem 5 Let X be a random variable, uniformly distributed on (0, 1), and let Y be a random variable uniformly distributed on (0, 2). With X and Y indepen dent. 1. Find the probability density of X + Y, fx+y. Co ownloaded by 100000798453237 from CourseHero.com on 11-08-2022 17:10:58 GMT -06:00 .com/file/127347966/Midtermpdf/ 2. Find the CDF of X + Y, Fx+y. Problem 6 Suppose a fair coin is flipped n times. Let X denote the number of heads in the n coin flips. Bound the probability P ( X 2 in 1. Applying Markov's inequality. 2. Applying Chebyshev's inequality