3. Suppose that Y ~ Bin(mk, Tk), k = 1,2 are two independent binomial random variables describing numbers of individuals with a certain disease in two groups. Let x be the group 1 indicator, that is, x = 1 if k = 1 and x = 0 if k = 2. Then consider the logistic regression. model log = 3n + Bik 1 k (a) Write down the likelihood for 30 and B. Derive the score vector S(3) where (Bo, B1), and the information matrix I(3). (b) Show that the (large-sample) asymptotic variance for B has the form 1 1 1 1 Var(B1) = + + + E(Y) E(m1 - Y) E(Y2) E(m2 - Y2) =