Suppose and that has a prior distribution. (a) Find m(x). (b) Show that, if m(x) is constant, then it must be the case that a = {3 = 1. (Stigler (1982) reports that this was the motivation for...

Suppose

and that

has a

prior distribution.

(a) Find m(x).

(b) Show that, if m(x) is constant, then it must be the case that a = {3 = 1. (Stigler (1982) reports that this was the motivation for the use of a uniform prior in Bayes (1763).)

Suppose, for

and that the Xj are independent.

(a) Find the ML-II prior in the situation of Exercise 24(a), for any given x.

(b) Find the ML-II prior in the situation of Exercise 24(b), for any given x.