Past exam of the mathematics course of the University of Cambridge / 2014 / iii / Paper 35 / 3 / a / Solution

At zero a centered normal distribution with standard deviation $\sigma$ has density $1/(\sqrt{2\pi }\sigma )$. The two prior standard deviations are $1/\sqrt{n_0}$ and $c/\sqrt{n_0}$, givingThe wider prior distribution has a lower density at its center.