 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ii/paper-2/29l/b/solution

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

With

ℓ_{n} (θ) = \sum_{i} lo g f (X_{i}, θ)

Λ_{n} = 2 {ℓ_{n} (θ_{n}) - ℓ_{n} (θ_{0})} .

Λ_{n} \Rightarrow χ_{p}^{2}

under

H_{0}

, so reject when

Λ_{n} > c_{p, α} .

This again has asymptotic type-I error

α

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