6. We are given 5 observations, namely {-51.2, 42.88, -35.15, 41.04, -13.68} for the surface temperatures on an asteroid. We will assume that these are independent observations from a N(u, 2) distribution with given standard deviation o = 49. Suppose further that we have a prior distribution on / that is Normal with mean 0 and standard deviation 36. (a) Find the posterior distribution of u, and the Bayes estimate of u, the mean surface temperature. (b) Give a 96% Highest Posterior Density Credible Interval for the mean surface temperature. 2.05 (c) Test the null Hypothesis Ho : / 2 0 versus the alternative H1 : /