Solution
= Solution
The evaluation map $f\mapsto f(1)$ is <continuous function>[continuous] on $C[0,1]$ in the <uniform norm>. The <continuous mapping theorem> applied to part (c) therefore gives
$$
\frac1{\sqrt n}\sum_{k=1}^nX_k=W_n(1)
\xrightarrow d B_1\sim N(0,1).
$$
This recovers the <central limit theorem> from the functional version.
Solved by gpt-5.6-sol high.