WOLFRAM|DEMONSTRATIONS PROJECT

The Exponential Distribution

​
parameter λ
1.
mean:
1
λ
=
1.000
variance:
1
2
λ
=
1.000
moment generating function:
λ
λ-t
=
1.
1.-t
The waiting time to observe the occurrence of an event in a Poisson process with intensity
λ
is a random variable that follows the exponential distribution with parameter
λ
(which must be positive). The exponential distribution is a special case of the gamma distribution with parameters
α=1
and
β=1/λ
. The red vertical segment marks the mean of the distribution.