Q3. [20%] (a) (19) Let X1, X2, X3, X4 be a random sample from a population that has mean u and variance (:2. Find E [(Xl-X2)2] and hence the value of k such that T = k[(X1-X2)2 + (x3-x4)2] is an unbiased estimator of 02. [6 marks] Xi, X2, ....Xl1 is a random sample from a uniform distribution U(0,u). Suppose that we consider the following three statistics, the latter two of which are used as estimators of the parameter or. Tn = sample maximum Un=aTrl Vn=b X , where a, b are constants. You are given the following results. 2 nor 1'10. Beam\"), \"Wm Also given is that U11 and Vn are both unbiased estimators of the parameter 01. Answer the following questions. You must give all your working and the steps involved with reasons. (i) Find the values of the constants a and b. [6 marks] (ii) Show that UI] and Vn are consistent estimators of the parameter 0:. Which of the two estimators (Un or Vn) would you expect to perform better and explain why, by giving a reason? [8 marks]