Let us calculate the probability that a sample from the Gaussian distribution
will fall within a single standard deviation 
of the mean 
:
Similarly, the probability that the sample is within two standard deviations
(within ``
'') of the mean is
Hence 68% of the samples will, on average, fall within one 
, and over
95%
of the samples will fall within two 
of the mean 
.
The Gaussian distribution will be encountered frequently in this course, not only because it is a fundamental pdf for many physical and mathematical applications, but also because it plays a central role in the estimation of errors with Monte Carlo simulation.
