8. Suppose that Y is a normal random variable with mean μ = 3 and variance σ2 = 1; i.e., Y-t N(3,1). Also suppose that X is a binomial randon variable with-2 and p-, 1/4; ie, dist x et Bin(2,1/4). Suppose X and Y are independent randon variables. Find the expected dist value of Yx. Hint: Consider conditioning on the events {X = j} for j = 0, 1, 2.