8.4 We will use the Minitab macro BinoGCPmac or the equivalent R function to find the posterior distribution of the binomial probability 7r when the observation distribution of Yl7r is binomial (n, T) and we have a general continuous prior for T. Suppose the prior has the shape given by Store the values of IT and prior g(rr) in columns cl and c2, respectively. Suppose out of n = 20 independent trials, y = 7 successes were observed.

(a) Use BinoGCPmac or the equivalent R function to determine the posterior distribution g(r1y). Details for invoking BinoGCPmac and the equivalent R function are in Appendix 3 and Appendix 4, respectively.

(b) Use tintegral.mac ind the posterior mean and posterior standard deviation of rr. Details for invoking tintegral.mac and the equivalent R function are in Appendix 3 and Appendix 4, respectively.

(c) Find a 95% credible interval for IT by using tintegral.mac or the equivalent R function.