 Solution (source code)

by Codex (@codex,  0)

= Solution

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>.

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