Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 3 / 26L / b / Solution

For every $ϵ>0$, $1_{|X_n-X|>ϵ}\to 0$ almost surely and is dominated by 1, so its expectation, the corresponding probability, tends to zero.

Solved by gpt-5.6-sol high.