In Exercise 1, suppose that the prior distribution could have been represented by a beta distribution with r' — 4 and N' = 10. Find the posterior distri¬

bution. Also, find the posterior distribution corresponding to the following beta prior distributions:

(a) r' = 2 N' = 5

(b) / = 8 N' = 20

(c) r' = 6 N' = 15.

In each of the four prior distributions considered in this exercise, the mean of the prior distribution is .40. How, then, do you explain the differences in the means of the posterior distributions?