Question 6: Suppose that we have a random sample of size n from a Bernoulli() distribution. We will use a complementary log-log model: A = cloglog(7) = log(- log(1 - )). The mle (maximum likelihood estimate) for 0 is 0 = log(- log(1 - #)), where 7 = (number of successes)/ (number of trials) is the sample proportion. (a) Use the delta method, to show that the estimated variance for 0 is VIe] = n (1 - ) log(1 - #)]2. (b) Using (a), compute the estimated (asymptotic) variance for cloglog(it), if the sample proportion is * = 0.25 with n = 100. (c) Suppose that it = y = 0.25, with n = 100. Give the 95% cloglog confidence interval for 7, which is obtained by first computing the 95% Wald interval for cloglog(7) and evaluating the limits of the interval in the inverse function of the cloglog