Work out the details for obtaining expressions (4.3.9)– XXXXXXXXXXin Example 4.3.1. Using XXXXXXXXXXshow that the marginal distribution of X and the posterior density of p are given by f (x) and f...

Work out the details for obtaining expressions (4.3.9)–(4.3.11) in Example 4.3.1.

Using (4.3.12) show that the marginal distribution of X and the posterior density of p are given by f (x) and f (p|x), respectively, define after (4.3.12). Hence, obtain the mean of the posterior density f (p|x) and show that the Bayes estimator of p is given by (a + x)/(a + b + n).