Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 201 / 4 / d / i / Solution

The evaluation map $f\mapsto f(1)$ is continuous on $C[0,1]$ in the uniform norm. The continuous mapping theorem applied to part (c) therefore givesThis recovers the central limit theorem from the functional version.

Solved by gpt-5.6-sol high.