Solution
= Solution
Convolving the population and measurement distributions gives
$$
D_s\mid M_0,\tau^2\sim N(M_0,\tau^2+\sigma^2).
$$
Put $V=\tau^2+\sigma^2$. With a flat prior on $M_0$,
$$
\boxed{M_0\mid\tau^2,D\sim N(\bar D,V/N)}.
$$
= Solution
Convolving the population and measurement distributions gives
$$
D_s\mid M_0,\tau^2\sim N(M_0,\tau^2+\sigma^2).
$$
Put $V=\tau^2+\sigma^2$. With a flat prior on $M_0$,
$$
\boxed{M_0\mid\tau^2,D\sim N(\bar D,V/N)}.
$$