Please see the question in the attached picture.

1. Assume X1, . . . ,Xn are i.i.d. N(p.,02) where both it and 02 are unknown. Find the marginal posterior for pt, assuming the prior pm, Org) = pmlaglal where p(0'_2) : 602, 02 > El. You will need to use a change of variables to nd p[02). Also, assume that pmla) = (27T0'2]_1'l2 exp{p2/(202]}. You may ignore constants of proportionality. Can you identify which type of distribution this marginal posterior density represents? Show your work (do not use symbolic computation soft- ware)