Suppose X1, . .., Xn are iid random variables from Bernoulli(p1 ) and Y1, ..., Yn are iid random variables from Bernoulli(p2). Further we assume that X1, . .., Xn and Y1, . .., Yn are independent. Let Xn = EL-, Xi and Yn = EL, Yi. Our interest is to test Ho : p1 = p2 versus HA : PI * P2. (a) We first consider the Wald-type test. (a.1) Show that vm { (108 Xn Yn P1 P2 1 - Yn - N(0, 2 ) 1 - Xn log log 1 - p1 - log 1 - P 2 in distribution. In your answer, please clearly indicate the form of n' in terms of p1 and p2. (a.2) Construct a consistent estimator n- for n2. (a.3) What is the limiting distribution of the Wald-type test statistic Wn = Vn (log Xn - log Yn) under Ho : P1 = p2