Consider the usual multiple regression model. Let F = X TX and T1/2 its (symmet- ric) square root. (a) Show that F\"? (E )3) E RP+1 is normal and specify its mean and covariance. (b) Let 11.2 = (3 ,9)TF(/ B). Find the distribution of 152/02. (C) Is 11:2 in the previous part independent of 32? Here 32 : ||e||2/(n p 1) is our usual unbiased estimate of 0'2. ((1) Show that ; is F distributed Where you specify the degrees of freedom