Please help to solve part (c), (d) and (e). Detailed steps are required. Thanks!

2. Suppose that we have the model yu ~ N(u, T-!) where T > 0 is known and / is an unknown parameter. (a) Write down f(ylu) (2 marks) (b) Show that flylu) x exp (-?(3-1)2) (3 marks) (c) Suppose that we have a prior / ~ N(a, b-!) where b > 0. Show that the prior distribution (/) verifies T (M) x exp b 2 ( 1 - a ) 2) (3 marks) (d) Show that the posterior (uly) verifies b T (uly) x exp T+ b T 2 b+T b+ (8 marks) (e) Which distribution is "(uly)? (3 marks) (f) Suppose that T = a = b = 2. Suppose that you observe a realization of y with a value of 2. Compute the posterior distribution (#|2) and explain how it relates to T (M). (6 marks) (g) Suppose now that you observe a second realization of y with a value of -2. Update the posterior 7(M|2) to incorporate this new information