Let X1,...,Xn be iid Poisson(A), and let A have a gamma(a,) distribution, the conjugate family for the

Let X1,...,Xn be iid Poisson(A), and let A have a gamma(a,β) distribution, the conjugate family for the Poisson. In Exercise 7.24 the posterior distribution of A was found, including the posterior mean and variance. Now consider a Bayesian test of H0: λ < λn vs H1: λ > λ0. 
(a) Calculate expressions for the posterior probabilities of Ho and Hi.
(b) If α = 5/2 and β = 2, the prior distribution is a chi squared distribution with 5 degrees of freedom. Explain how a chi squared table could be used to perform a Bayesian test.