Exercise 3 (3 + 3 points). Independence 1. Let X ~ Gamma(a, A) and Y ~ Gamma(, A) and suppose X and Y are independent. It can be shown (you don't have to prove this!) that X + Y is independent of X/(X + Y). Using this fact, prove that E X E(X) X +x E( X + Y ) 2. Suppose I roll two fair dice independently and define X to be the maximum value observed and Y to be the minimum value observed. Without doing any algebra, explain whether X and Y are independent