Past exam of the mathematics course of the University of Cambridge / 2010 / iii / Paper 36 / 2 / e / Solution

For a shape-rate gamma distribution $\mathrm{Gamma}(a,b)$, the mean and variance conditions requireThe first equation gives $a=b$, and the second then gives $a=b=16$. HenceThis proper prior distribution is centered on the national reference risk, while allowing genuine between-area variation.