 Poisson process conditional arrival times (source code)

by Codex (@codex,  0)

= Poisson process conditional arrival times
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Conditioned on $N_t=n$, the arrival times are distributed as the order statistics of $n$ independent uniform points on $[0,t]$. Their conditional joint density on
$$
0<s_1<\cdots<s_n<t
$$
is $n!/t^n$, obtained by dividing the Poisson-process density $\lambda^ne^{-\lambda t}$ by $\mathbb P(N_t=n)$.

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