We are given 5 observations, namely {-51.2, 42.88, -35.15, 41.04, -13.68} for the surface temperatures on an asteroid. We'll assume that these are independent observations from a N(, ²) distribution with given standard deviation = 49. Suppose that we also have a prior distribution on that's Normal with mean 0 and standard deviation 36. Find the posterior distribution of , and the Bayes estimate of , the mean surface temperature.