Problem 1: Let X and Y be random variables with joint density function : {2x² + y³, 0, Find the covariance of X and Y f(x, y) = 0 < x, y < 1 elsewhere

2. Let X and Y be two independent exponential random variables with parameters both equal to 3. (a) Find f(x, y), the joint probability density function of X and Y. (b) Let A = {(x, y) = R² : x > 4 and y > 5}. Find P(A). (c) Let B = {(x, y) = R² : x + y ≤ 2}. Find P(B).