Question

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(μ, σ*) distribution with given standard deviation σ-49. Suppose further that we have a prior distribution on μ that is Normal with m ean 0 and standard deviation 36. (a) Find the posterior distribution of μ, and the Bayes estimate of μ, the mean surface temperature. (b) Give a 96% Highest Posterior Density Credible Interval for the mean surface 2.05 temperature. (c) Test the null Hypothesis Ho : H 20 versus the alternative H: <O. (d) If only 2 values of u namely 0 and 1 are possible and have prior probabilities 2/3 , andia,respectively, test Ho : μ 0 versus Hi : μ-l ( (10+5+10+5-30)

Answer 1

Note:As per HOMEWORKLIB RULES three bits enough.Due to insufficient time i couldn't solve d bit.If you want to answer d bit please post it separately i will answer it. Thank you.