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 = EM Yi. Our interest is to test Ho : P1 = p2 versus HA : PI * P2. (b) We consider the likelihood ratio test for testing Ho : P1 = p2 versus HA : P1 * P2. (b.1) Show that the likelihood ratio test Rn = 2 { max In(P1, P2) - max In(P, p) P1 , P2 P for Ho : P1 = p2 versus HA : P1 + p2 has the following form: Rn = 2n{g(Xn) + g(Yn) - 29(0.5Xn + 0.5Y,) } for some smooth function g(x). In your answer, clearly indicate the form of g(x). (b.2) Derive the limiting distribution of Rn under Ho : P1 = P2. Note: directly use the results about the likelihood ratio test will not get any credit