We consider the case when y N(X,2V), where V is a known general positive definite matrix, and 2 is unknown.

For this model, we have introduced that the BLUE is = (XV 1X)1XV 1y, and an unbiased estimator for 2 is s2 = (y X)V 1(y X)/(n p 1).

Now, we want to derive a test statistic for H0 : =0 versus H1 : !=0.

(a) Find the distribution of .

(b) According to the distribution of , show that (XV 1X)/2 follows a chi-square distribution