- Problem 6 You Shall Use Calculator In Completing This Problem Express Your Solution Up To 3rd Decimal Place A Pair 1 (123.88 KiB) Viewed 10 times
Problem 6*. (You shall use calculator in completing this problem. Express your solution up to 3rd decimal place.) A pair of random variables (X, Y) has joint density that is proportional to (x+y)e¬x²-y, and f = 0 else. (a) Find the joint density f of (X, Y). x, y = [0, ∞) ², (b) Find the expected value and variance of X, Y. (c) Compute the covariance Cov(X, Y). Subsequently, compute the variance of 3X – 2Y. (d) Suppose Y = 1. Compute the conditional probability E[X|Y = 1] and conditional variance Var[XY = 1].