5.4 The exponential distribution (continuous)

Suppose an event occurs according to a Poisson process. Then the time between events has an exponential distribution.

Definition 5.4 (Exponential distribution) The exponential distribution with mean $\mu$ has PDF \[ f_X(x) = \frac{1}{\mu} \exp\left(-\frac{x}{\mu}\right)\qquad\text{for $x>0$} \] for $\mu > 0$.