 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ib/paper-1/18h/d/solution

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

The two tests have the same size, but their powers cross. At

θ = 0.1

π_{1} (0.1) = 0.15, π_{2} (0.1) = \frac{1}{2} (\frac{1}{10} + 0.2)^{2} < 0.15.

θ = 0.5

π_{1} (0.5) = 0.55, π_{2} (0.5) = 1 - \frac{1}{2} (1 - \frac{1}{10})^{2} > 0.55.

neither Test 1 nor Test 2 is uniformly most powerful .

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