Extension of Theorem 5.5-1] If X1, X2, . .., Xn are n independent normal variables with means /1, /2, . .., Un and variances or, oz,..., o? respectively. (a) Show the MGF of a; Xi + bi is given by MaiXitbi (t) = e(aimi+bi)t+ za,of+2 (b) Using the MGF Technique, prove the following result. n n Y = E(aiXit bi) ~ N (aiki + bi), ) = 1 i=1 where a1, a2, ..., an and b1, b2, ..., bn are constants