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