 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ii/paper-1/30k/a/solution

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

For

X = θ^{T} Z

E X = θ^{T} b, Var (X) = θ^{T} V θ .

The objective has gradient

b - V θ

and Hessian

- V

, which is negative definite. Its unique maximizer is therefore

θ_{M} = V^{- 1} b .

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