9.5 In the same study of water quality, n = 176 samples were taken from streams having a high environmental impact from sheep farming. Out of these y = 24 had a high Campylobacter level. Let T be the true probability that a sample of water from this type of stream has a high Campylobacter level.

(a) Find the frequentist estimator for 7r.

(b) Use a beta (1,lO) prior for T. Calculate the posterior distribution g(~ly).

(c) Find the posterior mean and variance. What is the Bayesian estimator for T?