Question: (Normal Distribution) Suppose n is a fixed, positive, constant number. Define a random variable Y to be Y = X1 + X2 + + Xn

(Normal Distribution) Suppose n is a fixed, positive, constant number. Define a random variable Y to be Y = X1 + X2 + + Xn n . Suppose all of the X's follow the same normal distribution, each with the same mean and the same variance 2 , so X1 N(, 2 ); X2 N(, 2 ); . . . Xn N(, 2 ). 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

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