Suppose that X1, , Xn form a random sample from the normal distribution with unknown mean and unknown precision , and also that the joint prior distribution of and is the normal gamma distribution satisfying the following conditions E() 1, Var( ) 1 3, Pr( 3) 0 5, and Pr( 0 12) 0 9 Determine the pri...

Since E 0 0 1 and Var 0 2 0 13 it follows that 0 0 3 Also since the distribution of is symme ...

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 also that the joint prior of μ and τ is the normal-gamma satisfying the following conditions: E(τ) = 1, Var(τ ) = 1/3, Pr(μ > 3) = 0.5, and Pr(μ > 0.12) = 0.9. Determine the prior hyperparameters μ0, λ0, α0, and β0.
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...