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

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

+1 9