Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 2 / 29J / a / Solution

The Kolmogorov-Smirnov theorem states that, for continuous $F$,where $B$ is a Brownian bridge; the finite-sample law is also independent of continuous $F$. To test $H_0:F=F_0$, computeand reject when $\sqrt{n}{D}_n$ exceeds the appropriate null quantile.