 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2018/ii/paper-3/28k/a/solution

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

f (x, θ)

θ_{0}

I (θ_{0}) = E_{θ_{0}} [\nabla_{θ} lo g f (X, θ_{0}) \nabla_{θ} lo g f (X, θ_{0})^{T}] .

Here

lo g f (x, θ) = constant - \frac{1}{2} ∥ x - θ ∥^{2}, \nabla_{θ} lo g f (x, θ) = x - θ .

Since

Cov_{θ_{0}} (X) = I_{p}

I (θ_{0}) = I_{p} .

The information in the full independent sample is

n I_{p}

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