Question: QUESTION 3 3.1. Consider a general linear model ???? = ???????? + where is distributed with mean ???? = ???? and variance ???? = ????

QUESTION 3 3.1. Consider a general linear model ???? = ???????? + where is distributed with mean ???? = ???? and variance ???? = ???? ???? ????, and ???? is distributed with mean ???????? and variance ???? ???? ????. The normal equations for ???????? not of full rank are ???? ???????? = ???????? For any generalized inverse ???? of ????????, the corresponding solution is given by ???? = ???????? ???? 3.1.1. Determine the expected value and the variance of ????. (5) 3.1.2. Determine the residual sum of squares. (5) 3.2. Suppose that the random vector x has a multivariate normal distribution with moment generating function ???????????? = ???? ???? ???? ???????? ???? + ???? ???? ???????? 3.2.1. Determine the moment generating function of the linear model. (4) 3.2.2. What is the distribution of the linear model?

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