If X has a Poisson distribution and the prior distribution of its parameter (capital Greek lambda) is a gamma distribution with the parameters and , show that (a) The posterior distribution of given X x is a gamma distribution with the parameters x and 1 (b) The mean of the posterior distribution o...

If X has a Poisson distribution and the prior distribution of its parameter (capital Greek lambda) is

Question:

If X has a Poisson distribution and the prior distribution of its parameter Λ(capital Greek lambda) is a gamma distribution with the parameters α and β, show that

(a) The posterior distribution of given X = x is a gamma distribution with the parameters α + x and β/β + 1 ;

(b) The mean of the posterior distribution of Λ is

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...