Sequential two-step waiting time
= Sequential two-step waiting time
{title2=$p(t)=\frac{ab}{a-b}(e^{-bt}-e^{-at})$}
For independent exponential waits of rates $a$ and $b$, their sum has density $ab(e^{-bt}-e^{-at})/(a-b)$, obtained by convolution on $[0,t]$. The limit at $a=b$ is $a^2te^{-at}$ and the mean is $a^{-1}+b^{-1}$.