Derive the posterior distribution for A given (x1, , xn) up to a proportional constant. Suppose we draw an i.i.d. sample X1, ..., Xn from a Poisson (2) distribution, where ) is a parameter of unknown value. The pdf of the Poisson (2) distribution is f ( xi ) = xi! Suppose that 1 is treated as a random variable, and the prior distribution for 1 is Gamma, i.e. 2 ~ Gamma (a, B). The prior pdf for A is Ba TT (2 ) = ja-1e-Ba for 2 > 0. r(a)