The Exponential distribution
is often used to model situations involving the random time
between arrivals to a service facility. When the
average arrival rate is and the
arrivals occur independently, then the time between arrivals
has an Exponential distribution characterized
by the single positive parameter .
The density has the shape shown in the figure.
Integrating the density yields a closed form expression for
the CDF. The distribution has equal mean and standard deviation,
and the skewness is always 4. Because it is skewed
to the right, the mean is always greater than the median. The
probability that the random variable is less than its mean
is independent of the value of .