Please verify the following two facts, which will be used to develop inference in regression models: (i) If Y is a normally distributed random variable, then Y' = a + cy (a and c are constants) is normally distributed with mean a + cE(Y ) and variance c'Var(Y). (ii) If Y1, ..., Yn are independent normal random variables, the linear com- bination al Y1+ . . . + anYn is normally distributed, with mean E a; E(Y:) and variance Caz Var(Yi)