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 x to fall within of
, even though
the actual range of samples x 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 .
Figure 6: Exponential pdf.