. [20 pts) Suppose we have a sample {K,X}'=1 of i.i.d. observations and we assume the model Y = 51X + E with E[e|X] = 0 and Var(E|X) 2 0'2. Unlike the standard model, we have no constant (equivalently, we assume the constant is zero). In this problem we will study the properties of the estimator 1 n b . . - _ y; Xib* 2' 1 mimmizes n if 1) Throughout the problem it may be helpful to review our arguments we saw in class for the standard linear regression estimation (which includes a constant). (a) Solve the rst order conditions for the stated minimization problem to show In satises 2 2:1 YXi 2 n I\" n. :3? KX EZmXMFM2X351=Zmabl=H1X2- 21:1 15:1 i=1 i=1 a (b) Let w; = X's/22:1 X3. Using your answer to part (a) show that bl = ,6] + Bi mm. (c) Treating the {we}?=1 as constants, what is E[b1]? (d) Treating the {wdng as constants, what is Var(b1)