Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 207 / 5 / b / ii / Solution

Condition on the independently generated random censoring information. For every realized common censoring horizon, part b(i) gives the same conditional probability ${\lambda }_1/({\lambda }_1+{\lambda }_2)$. The law of total probability therefore gives that ratio after averaging over the censoring distribution as well.