Consider linear regression model 3; : n + 23:1 jmj + E with the transposed design matrix X T given by ## [,1] [,2] [,3] [,4] [,5] ## x1 0 1 o 1 1 ## x2 0 1 1 1 o and the transposed response vector yT given by ## [,1] [,2] [,3] [,4] [,5] ## y 3 1 4 5 3 The noise vector 5' : [61, . . . 1'9an follows the following model: {n : 5) 6'1 : Zl EgE'g_1=Z, i=2,...,n 3' . Z~N(0,E), 11,...,n. Assume that {Z1, Z2, . . . , Zn} are independent. (a) What is the distribution of s = [1,52, . . . ,Ean? (b) What is the smallest possible variance of an unbiased estimate of [32