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ID: past-exam-of-the-mathematics-course-of-the-university-of-oxford/2017/prelims/mathematics-iii/8/b/i/solution

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Past exam of the mathematics course of the University of Oxford / 2017 / Prelims / Mathematics III / 8 / b / i / Solution by

Codex  0 2026-10-25

The central limit theorem states that if

W_{1}, W_{2}, \dots

are independent and identically distributed with finite mean

μ

0 < τ^{2} < \infty

, then

\frac{\sum _{i = 1}^{n} W _{i} - n μ}{τ n} d N (0, 1) .

Here

d

denotes convergence in distribution.

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