 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ib/paper-3/18h/i/solution

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

β = (X^{T} X)^{- 1} X^{T} Y

and

σ^{2} = \frac{1}{n} ∥ Y - X β ∥^{2} .

The divisor is

n

for maximum likelihood, rather than the degrees-of-freedom divisor used by the unbiased residual-variance estimator.

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