Please provide detail process, thanks

2. Let X1, ..., Xn be iid draws from N(#, o?). (a) Show that the joint density at (21, . .., In) is proportional (with respect to () to exp 1 (#-2)2 with 2 := 1 Er;. In other words, verify that all the other factors in the joint density don't involve /. Hint: Remember the bias-variance decomposition for data that you worked out in Homework 2 Problem 2.] (b) Treat o as known, and consider the N(0, y?) prior distribution for . Use your results from Problem 2 (a) and Problem 1 (b) to find the posterior distribution for /. [Hint: (u - X) equals (2 - 2Xu plus a term that doesn't involve /.] (c) Is it possible for the posterior distribution of a to have a larger variance than the prior distribution of /