Let be the OLS estimator in (1), where the design matrix X has full rank p

Let βˆ be the OLS estimator in (1), where the design matrix X has full rank p

(a) Find var(βˆ

1 − βˆ

2 |X), where βˆ

i is the ith component of βˆ.

(b) Suppose c is p×1. Show that E(c

βˆ|X) = c

β and var(c

βˆ|X) =

σ2c

(X

X)−1c.