 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ib/paper-3/18h/a/solution

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

- \frac{n}{2} lo g σ^{2} - \frac{1}{2 σ ^{2}} (Y - Xβ)^{T} Σ_{0}^{- 1} (Y - Xβ) .

β = (X^{T} Σ_{0}^{- 1} X)^{- 1} X^{T} Σ_{0}^{- 1} Y,

and maximizing over the scale gives

σ^{2} = \frac{1}{n} (Y - X β)^{T} Σ_{0}^{- 1} (Y - X β) .

n

is appropriate for maximum likelihood rather than unbiased estimation.

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