 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ii/paper-1/29k/c/solution

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

S_{σ} (X) = - \frac{1}{σ} + \frac{X ^{2}}{σ ^{3}} .

Its variance, or equivalently minus the expected second derivative of the log-likelihood, is the Fisher information

I (σ) = \frac{2}{σ ^{2}} .

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