Conditioning on $T_1=t$ and using <independent random variables> gives
$$
\mathbb P(T_1<T_2)
=\int_0^\infty
\mathbb P(T_2>t\mid T_1=t)f_1(t)\,dt
=\int_0^\infty f_1(t)F_2(t)\,dt,
$$
where the notation in the paper uses $F_2$ for the <survival function>.

Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 207 / 5 / a / i / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/iii/paper-207/5/a/i/solution