 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-2/31k/d/solution

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

Each

Z_{j} = n^{- 1} \sum_{i} ε_{i} X_{ij}

1/ n

-sub-Gaussian. Applying the exponential-moment bound to the

2 p

variables

\pm Z_{j}

and optimizing the parameter gives

E max_{j} ∣ Z_{j} ∣ \leq 2 lo g (2 p) / n

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