5.4 Jeffreys' prior: For sampling models expressed in terms of a p-dimensional vector , Jeffreys' prior (Exercise 3.11) is defined as py() xx VI(4)|, where I() | is the determinant of the p x p matrix I() having entries I(2/) k,1 = -E[02 log p(Y |2/) / 24/k.Or/i]. a) Show that Jeffreys' prior for the normal model is py (0, 2) ac (02)-3/2. b) Let y = (y1, ...,Un) be the observed values of an i.i.d. sample from a normal(0, o2) population. Find a probability density py(0, o2ly) such that py(0, o'ly) x pJ(0, o2)p(y|0,02). It may be convenient to write this joint density as py(0|02, y) x pJ(oly). Can this joint density be considered a posterior density