The bus may have arrived before observation began or after observation ended. Its compatible event set is $(-\infty,2)\cup(20,\infty)$, so, with endpoint conventions chosen to match whether arrivals exactly at 2 or 20 would be seen, the contribution is
$$
\mathbb P(T<2)+\mathbb P(T>20)=F(2^-)+S(20).
$$
This is <doubly censored data>, because neither the side nor the event time is known.

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 207 / 6 / a / v / Solution

Doubly censored data leave an event known only to lie outside an observation interval, without revealing whether it occurred before observation began or after observation ended.


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