If X has a Poisson distribution and the prior dis-tribution of its parameter (capital Greek lambda) is a gamma distribution with the parameters α and β,show that(a) the posterior distribution of given X = x is agamma distribution with the parameters α + x and ββ + 1;(b) the mean of the posterior distribution of is μ1 = β(α + x)β + 1

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.