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2. Consider the linear regression model K=o+1X+u1 t:1,2,...,n, where X: 3-9 [I for all t and at is a random disturbance such that Efug} = U for all t. (a) Suppose that E[Xu} = {l for all t, Efmna) = [l for all t r s, and ag} 2 023*, where 0'2 3:- [l is an unknown constant and E; 3:- [l is an observable non stochastic variable. Explain how to estimate ,5 = [,1}' efciently when: {i} 3: = 2 for all t; {ii} 3t 2 Xf. Include in your answer a careful explanation of why your proposed estimation method would produce an eicient estimate of in each case. [30%] {b} Suppose that at = the\"; + st, where {in is a known parameter and st are unobservable random variables such that st} = G, EDS?) = a: 33- , E(EE3) = [l for all t 9E s, and E(XtEa} = [l for all t and 5. Explain how to estimate ,5 efciently. Include in your answer a careful explanation of why your proposed estimation method would produce an eici-t estimate of ,5. [2U%]