 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-oxford/undated/prelims/mathematics-iii-resit/7/c/i/solution

ϵ = (ϵ_{1}, \dots, ϵ_{n})^{⊤}

Σ = E [(ϵ - E ϵ) (ϵ - E ϵ)^{⊤}], Σ_{ij} = Cov (ϵ_{i}, ϵ_{j}) .

Its diagonal entries are variances, and its off-diagonal entries measure pairwise covariance. Finite second moments make every entry well defined.

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