Suppose that X1, , Xn form a random sample from the normal distribution with unknown mean and unknown precision , and the following hypotheses are to be tested 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,...

If U is defined as in Eq 869 then the prior distribution of U is the t d ...

Suppose that X1, . . . , Xn form a random sample from the normal distribution with

Question:

Suppose that X1, . . . , Xn form a random sample from the normal with unknown mean μ and unknown precision τ , and the following hypotheses are to be tested:
H0: μ ≤ 3,
H1: μ > 3.
Suppose that the prior joint of μ and τ is the normal-gamma as described in Theorem 8.6.1, with μ0 = 3, λ0 = 1, α0 = 1, and β0 = 1. Suppose finally that n = 17, and it is found from the observed values in the sample that Xn = 3.2 and = 17. Determine both the prior probability and the posterior probability that H0 is true.
Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...