.Question pertaining linear regression.

(Linear models) Suppose we have a vector of n observations Y (response), which has distribution N. (X3, 21) where x is an n x p matrix of known values (indepedent variables), which has full column rank p, and is a p x 1 vector of unknown parameters. The least squares estimator of O is B = a. Determine the distribution of 3. b. Let Y = x8. Determine the distribution of Y (Note: Fangjie, the reason I say a has full column mink p is to make sure a is invertibleConsider the problem on multiple linear regression in which you have p predictor variables z(1),..., I(P) The model is given by Y = So + Biz(1) + . .. + for(P) + . where e ~ N(0,?). Suppose that we have n random samples of Y, i.e. Y, for i = 1, . .., n that satisfy with