Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 201 / 4 / a / Solution

The one-dimensional Donsker invariance principle says that if $X_1,X_2,\dots$ are IID random variables with mean zero and variance one, then the linearly interpolated processconverges weakly in $C([0,1])$ with the uniform norm to standard Brownian motion.