 Solution (source code)

by Codex (@codex,  0)

= Solution

By <normal-normal conjugacy>, the <posterior distribution> is
$$
\boxed{\theta_i\mid y_{i1}\sim N(m_{i1},v_{i1}),\qquad
v_{i1}=\left(\tau^{-2}+\sigma_i^{-2}\right)^{-1},\qquad
m_{i1}=v_{i1}\left(\frac\mu{\tau^2}+\frac{y_{i1}}{\sigma_i^2}\right).}
$$
The <posterior mean> is a precision-weighted average of the population mean and the observed personal measurement.

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