Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 3 / 28L / c / Solution

Replace the two $G$ quantiles by conditional bootstrap quantiles ${\hat{q}}_u$ in the interval from (a). Uniform convergence implies ${\hat{q}}_u\to q_u$ in probability at continuity points, so Slutsky and continuity of $G$ give coverage tending to $1-\alpha$.

Solved by gpt-5.6-sol high.