D.1. The joint probability density function of X and Y is given by f(:r,y) = c[(:1: 3:2) +my2] 0 1/2, given that Y = y. (c) Find the probability that Y > 1/4, given that X = 3/4. D.2. If X and Y are independent and identically distributed standard normal random vari- ables, compute the joint density of U = X + Y, V = Y/ X . 3.1. In a classroom, quizzes are collected, shuffled, and then randomly handed back out to grade. What is the expected number of people who get their own quiz hack? 3.2. Consider a sample of size 3 from an exponential distribution with A = 5. (a) Find the expected value of the sample mean. (b) Compute the probability that the median is in the interval (0.1, 0.3)