This distribution can describe a number of physical phenomena, such as the
time 
for a radioactive nucleus to decay, or the time 
for a component
to fail, or the distance 
a photon travels in the atmosphere before
suffering a collision with a water molecule.
The exponential distribution is characterized by the single parameter
, and one can easily show that the mean and variance
for the exponential distribution are given by:
Figure 6 illustrates the exponential distribution. Note that the standard deviation of the exponential distribution is
Later we will learn that we can associate the standard deviation with a sort of
expected deviation from the mean, meaning that for the exponential
distribution, one would expect most samples to fall within 
of
, even though
the actual range of samples is infinite.
One can see this by computing the probability that a sample from the
exponential distribution falls within 
of
the mean 
Hence 83% of the samples from the exponential distribution can be expected
to fall within a half of a standard deviation of the mean, although some of the
samples will be far from the mean, since 
.
