A random sample of size 10 from a Poisson distribution with mean? yields the following data values: 3, 4, 3, 1, 5, 5, 2, 3, 3, 2 The prior distribution of lambda is Gamma(5,2). Calculate the Bayesian estimate of lambda under squared error loss. The above question is on page 712 of the 2022 CMP (e-book PDF) and for printout page 18 of the chapter. The final answer to the question is Gamma (36,12) while the likelihood function output is as C*[e^(-10*lambda)]*[lambda^(31)]. So the question which I have in this case is how did we obtain 36 and 12 for the final answer? Did we add 5 and 2 to the values of lambda & e and get the answer? Best, Naitik Shah.
Remember the posterior is proportional to the prior multiplied by the likelihood. That's why the parameters are not matching the likelihood on its own.
