16.1 We will use the Minitab macro BinoMixPmac or the equivalent R function to find the posterior distribution of T given an observation y from the binomial(n, T) distribution when we use a mixture prior for T. Suppose our prior experience leads us to believe a beta(7,13) prior would be appropriate.

However we have a nagging suspicion that our experience was under different circumstances, so our prior belief may be quite incorrect and we need a fall-back position. We decide to use a mixture prior where go(T) is the beta(7,13) and gI(.rr) is the beta(1,l) distribution, and the prior probability?