Q2 Consider a linear model: P Yi = Bo + Bitei, j=1 where M; and my are the maximum and minimum values of rij, ..., In; for j = 1,2, .... p - 1, and " N(0, o' ) with known of > 0. (a) Derive the maximum likelihood estimator (MLE) for (Bo, B1, . .., 8p-1)- (b ) Given the MLE (Bo, 1. .... 8p-1) from 2a and the predictor Y (x) = Bo+ ) ,x, B,, where X = (r1, . ..,Xp-1) , derive a 100(1 -0)% confidence interval for Y (x). (c) Find the x that gives the narrowest confidence interval in 2b