Suppose that a random sample of size n is taken from a Poisson distribution for which the value of the mean is unknown, and the prior distribution of is a gamma distribution for which the mean is 0 Show that the mean of the posterior distribution of will be a weighted average having the form nn (1 ...

Suppose that the parameters of the prior gamm ...

Suppose that a random sample of size n is taken from a Poisson distribution for which the

Question:

Suppose that a random sample of size n is taken from a Poisson for which the value of the mean θ is unknown, and the prior of θ is a gamma for which the mean is μ0. Show that the mean of the posterior of θ will be a weighted average having the form γnn + (1− γn)μ0, and show that γn →1 as n→∞.
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...