 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2008/iii/paper-44/3/c/solution

Codex  0 Created 2026-10-03 Updated 2026-10-14

θ_{i} ∣ y_{i 1} \sim N (m_{i 1}, v_{i 1}), v_{i 1} = (τ^{- 2} + σ_{i}^{- 2})^{- 1}, m_{i 1} = v_{i 1} (\frac{μ}{τ ^{2}} + \frac{y _{i 1}}{σ _{i}^{2}}) .

The posterior mean is a precision-weighted average of the population mean and the observed personal measurement.

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