Suppose Y = X + where (i) X is n p of rank p, and (ii)

Suppose Y = Xβ +  where

(i) X is n× p of rank p, and

(ii) E(|X) = γ , a non-random n×1 vector, and

(iii) cov(|X) = G, a non-random positive definite n×n matrix.

Let βˆ = (X X)−1X Y . True or false and explain:

(a) E(βˆ|X) = β.

(b) cov(βˆ|X) = σ2(X X)−1.

In (a), the exceptional case γ ⊥ X should be discussed separately.