1. Let X be a random variable with mean µ and variance σ2. Let Y = aX2 + bX + c. Find the expected value of Y .

2. Let X, Y , and Z be independent random variables, each with mean µ and variance σ2.

(a) Find the expected value and variance of S = X + Y + Z.
(b) Find the expected value and variance of A = (1/3)(X + Y + Z).
(c) Find the expected value of S2 and A2.

3. Let X and Y be independent random variables with uniform density functions on [0, 1]. Find
(a) E(|X - Y |).
(b) E(max(X, Y )).
(c) E(min(X, Y )).
(d) E(X2 + Y 2). (e) E((X + Y )2).