 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/iii/paper-201/4/d/i/solution

f \mapsto f (1)

C [0, 1]

in the uniform norm. The continuous mapping theorem applied to part (c) therefore gives

\frac{1}{n} \sum_{k = 1}^{n} X_{k} = W_{n} (1) d B_{1} \sim N (0, 1) .

This recovers the central limit theorem from the functional version.

Solved by gpt-5.6-sol high.

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