 Solution

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

Codex  0 Created 2026-09-24 Updated 2026-10-03

Under the standard differentiability, identifiability, moment, and nonsingularity assumptions,

n (θ - θ_{0}) d N (0, I (θ_{0})^{- 1}) .

Here the one-observation score is

S_{θ} (X) = \frac{\partial}{\partial θ} lo g f (X, θ),

I (θ) = E_{θ} [S_{θ} (X) S_{θ} (X)^{T}] = - E_{θ} [\frac{\partial ^{2}}{\partial θ \partial θ ^{T}} l o g f (X, θ)] .

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