exponential

The exponential distribution models the time between random independent events occurring at a constant average rate. It is defined by the following probability density function:

\[
f(x; \lambda) =
\begin{cases}
\lambda e^{-\lambda x} & \text{for } x > 0 \\\\[0.6em]
0 & \text{for } x \le 0
\end{cases}
\]