Let Y, Y2,..., Y, denote a random sample from a Poisson-distributed population with unknown mean . The related pdf is: f(y;|2) 23e-2 y;! The unknown parameter is assumed to be non-constant and follows a given distribution. We wish to use Bayesian method on . a) Prior distribution for the unknown parameter . State a possible choice for the prior distribution of and explain the advantages of such choice. Write the prior density function. b) Likelihood function for the Poisson-distributed random sample Y, Y2, ., Yn . n Find the joint density (likelihood function) of Y, Y2, ..., Yn, and write this write it as a function of Y i=1