 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ii/paper-1/29l/c/solution

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

For

0 \leq m \leq θ_{0}

P_{θ_{0}} (M_{n} \leq m) = (\frac{m}{θ _{0}})^{n} .

Hence, for

z \geq 0

P {n (θ_{0} - M_{n}) > z} = (1 - \frac{z}{n θ _{0}})^{n} ⟶ e^{- z / θ_{0}} .

Thus

n (θ_{0} - θ) d Z, Z \sim Exp (1/ θ_{0}) .

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