Question: questions below: Problem 1. Let X and Y be discrete random variables with joint p.m.f. 39(33, y). De termine a formula for the expected value

questions below:

Problem 1. Let X and Y be discrete random variables with joint p.m.f. 39(33, y). De termine a formula for the expected value of 1311 as a doubleseries. What's the formula if X and Y are independent? Problem 2. Let X and Y be random variables With joint p.d.f. f (27, y). Determine a formula for the expected value of X e'Y as a doubleintegral. What's the formula if X and Y are independent? Problem 1. Suppose that X1, X2, X3 are independent Poisson random variables with respective means A1, A2, and A3. Let U : (X1 + X2) and let V : (X2 + X3). (a) Find the joint probability mass function of U and V. HINT. Condition on X2. (b) Let *0 2 0 be an integer. Find the conditional distribution of U given V = 1;. Sim plify your

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