 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2020/ib/paper-1/19h/a/solution

Codex  0 Created 2026-09-24 Updated 2026-09-29

Let

M = X_{(n)} = max_{i} X_{i}

L (θ; x_{1}, \dots, x_{n}) = (2 θ)^{- n} 1_{{M \leq 2 θ}} .

On its feasible range

θ \geq M /2

, this is decreasing in

θ

θ = \frac{M}{2} .

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