Truncated exponential distribution
= Truncated exponential distribution
{title2=$f(u)=\frac{de^{-du}}{1-e^{-dt}}\mathbf1_{0<u<t}$}
Condition an <exponential distribution> of rate $d>0$ on falling below $t>0$. Normalizing its <probability density function> gives the displayed density. Integration gives <expectation> $1/d-t/(e^{dt}-1)$. As $d\downarrow0$, the density tends to the <uniform distribution> on $(0,t)$ and the <expectation> tends to $t/2$.
// Target: probability-and-statistics.bigb