Let $y$ be the sum of $n$ observations from a Poisson distribution with mean $\thetas. Let the prior for $\theta$ be a gamma distribution with parameters $\alpha$ and $\betas, parameterised as follows: $$ f(\theta)=\frac{\beta^{\alpha}} {\Gamma (\alpha)} \theta*(\alpha-1) e^{- \theta \beta), \quad 0 \leqslant \theta