## 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 5.2 (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 \(\mu>0\).