Suppose that X1,...,Xn form a random sample
Chapter 9, Problem 18(choose chapter or problem)
Suppose that X1,...,Xn form a random sample from the normal distribution with unknown mean and unkSuppose that X1,...,Xn form a random sample from the normal distribution with unknown mean and unk H0: 3, H1: > 3. Suppose that the prior joint distribution of and is the normal-gamma distribution, as described in Theorem 8.6.1, with 0 = 3, 0 = 1, 0 = 1, and 0 = 1. Suppose fi- nally that n = 17, and it is found from the observed values in the sample that Xn = 3.2 and n i=1(Xi Xn)2 = 17. Determine both the prior probability and the posterior probability that H0 is true.
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