Suppose that X1, , Xn form a random sample from the normal distribution with unknown mean and known variance 2 Suppose also that the prior distribution of is normal with mean and variance 2 a Determine the shortest interval I such that Pr( I X1, , Xn) 0 95, where the probability is calculated with ...

a The posterior distribution of is the normal distribution ...

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 θ and known variance σ2. Suppose also that the prior of θ is normal with mean μ and variance ν2.
a. Determine the shortest interval I such that Pr(θ ∈ I |X1, . . . , Xn) = 0.95, where the probability is calculated with respect to the posterior of θ, as indicated.
b. Show that as ν2→∞, the interval I converge to an interval I∗ that is a confidence interval for θ with confidence coefficient 0.95. 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...