Use delta method to find the following……………………..

(a) Let X be a. random variable with E(X) = 7 and E(X — 102 = Var(X). Let 9(X) = ln(X). Pleaseuse the delta. method to ﬁnd an approximation for Var (1n(X)). (b) Consider a. 2×2 table for a prospective study. Let nu ~ Binomial(n1+1 1r1) and let n21 ~ Binomial(n2+, 71",), Where ‘m; = P(Y = 1 1 X = 2′), 2′: 1, 2. An estimator for an is in = 311-: and similarl an estimator for 7r is fr = 221-. Assume n and n are inde endent. Recall in class we, 2 2 “2+ 11 21 1 3 used the delta method to ﬁnd an approximation for the momma) Le.1 the variance for the odds of an event. _n_ in Denote the odds ratio by 0 = -—1;—l— ; and let 0 = 1—:L be an estimator for 6. Note that1—1r2 1—fr2 001) (—“L. it.) = 0. Use the delta method to ﬁnd an approximation for var (11105)). 1—fr1 ’ 1—72