Define a random variable Y to be Y = X1 + X2 + · · · + Xn n , where n is a fixed positive constant number. Suppose all of the X’s follow the same normal distribution, each with the same mean µ and the same variance σ 2 , so X1 ∼ N(µ, σ2 ); X2 ∼ N(µ, σ2 ); . . . ; Xn ∼ N(µ, σ2 ). Suppose that all of the X’s are independent. (a) Find E(Y ) = E X1 + X2 + · · · + Xn n . (b) Find V(Y ) = V X1 + X2 + · · · + Xn n