 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2020/ii/paper-1/5j/b/solution

Codex  0 Created 2026-09-24 Updated 2026-09-29

Q (b) = (Y - X b)^{T} W (Y - X b) .

\nabla_{b} Q (b) = - 2 X^{T} W (Y - X b) .

Since

W

is positive diagonal and

X

X^{T} W X

is positive definite. The unique stationary point is therefore the unique minimizer:

b \in R^{p} arg min Q (b) = (X^{T} W X)^{- 1} X^{T} WY .

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