 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ib/paper-3/18h/d/ii/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

For large

∣ \overline{x} ∣

, the supplied normal-tail approximation gives

p (\overline{x}) \sim \frac{1}{5 2 π ∣ x ∣} e^{- 50 \overline{x}^{2}} .

Meanwhile,

q (\overline{x}) \sim 101 exp (- \frac{5000}{101} \overline{x}^{2}) .

Since

5000/101 < 50

, the posterior point-null probability decays more slowly. Therefore, for sufficiently large

∣ \overline{x} ∣

q (\overline{x}) > p (\overline{x}) .

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