 Solution

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

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

Write the new measurement as

Y_{i 1} = θ_{i} + ε_{i 1}

, with independent

θ_{i} \sim N (μ, τ^{2})

and

ε_{i 1} \sim N (0, σ_{i}^{2})

Y_{i 1} \sim N (μ, τ^{2} + σ_{i}^{2}) .

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