Consider the situation of Exercise 68. One prior that is entertained for the i.i.d. 1 is that they are   unknown. A second prior entertained is that they are i.i.d.   having a second stage K(3.30,...

Consider the situation of Exercise 68. One prior that is entertained for the i.i.d.

₁
is that they are

  unknown. A second prior entertained is that they are i.i.d.

having a second stage K(3.30, (0.03)2) distribution. In both cases, assume that nothing is known about O², and that it is given a constant second stage density. Find and compare the marginals under the two prior models. (Note that an improper prior is reasonable to use in such an endeavor only when it is the same parameters being given the improper prior in the cases being compared.)