Refer to Exercise 1.12 on estimating the population proportion of vegetarians. For the beta(0.5, 0.5) prior,

Refer to Exercise 1.12 on estimating the population proportion π of vegetarians. For the beta(0.5, 0.5) prior, find the Bayes estimator of π, show that the posterior 95%

interval is (0.00002, 0.0947), and show that the posterior P(π < 0.50) = 1.000.