Question: need help with this problem, thanks! 6. We are given 5 observations, namely {-51.2, 42.88, -35.15, 41.04, -13.68} for the surface temperatures on an asteroid.

need help with this problem, thanks!

need help with this problem, thanks! 6. We are given 5 observations,

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, 02) 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 , 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 : /

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