statistic

We are given 5 observations, namely {-51.20, 42.88, -35.15, 41.04, 13.68}, for the surface temperatures (in degrees Centigrade) on an asteroid. Assume that these are independent observations from a N (p502) distribution with given variance 02 = 49. Suppose further that we have a prior distribution on a that is Normal with mean 0 and variance 36. (a) Find the posterior distribution of p, and the Bayes estimate of p, the mean surface temperature. (b) Give a 96% Highest Posterior Density Credible Interval for the mean surface temper- ature. (c) Test the null Hypothesis H0 : p 2 0 versus the alternative H1 : ,u