Suppose that X1, , xm form a random sample from the normal distribution with mean 1 and variance 21, and Y1, , yn form a random sample from the normal distribution with mean 2 and variance 22 Suppose that we use the usual improper prior and that we wish to test the hypotheses H0 21 22, H1 21 22 a P...

a The null hypothesis can be rewritten as ...

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

Question:

Suppose that X1, . . . , xm form a random sample from the normal with mean μ1 and variance σ21, and Y1, . . . , yn form a random sample from the normal with mean μ2 and variance σ22 . Suppose that we use the usual improper prior and that we wish to test the hypotheses
H0: σ21 ≤ σ22,
H1: σ21 > σ22.
a. Prove that the level α0 F test is the same as the test in (9.8.7) when α0 = w1/(w0 + w1).
b. Prove that the p-value for the F test is 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...