Please complete the Question below:

It is often desirable for the mean and variance of a random variable to be unrelated, such as the normal distribution. This is clearly not true of the binomial distribution Where for Y N B (n, 7r), the variance is va.r(Y) :mr{1 71') : 1E(Y)(1 IE(Y)). The delta method can be used to motivate a transformation of p or 71' such that the resulting distribution will have constant variance. From the lecture notes, the estimator for the transformation g(7r) has asymptotic distribution map) ~ w 1W (0, (OT) vane) . (a) Suggest and justify a transformation 9 such that the variance is constant, i.e., (did)? rm) : constant. (b) Using the transformation 9 derived in part (b), derive the asymptotic distribution of 9(P) and demonstrate this distribution has constant variance