The Gaussian distribution is important in science
and statistics. Measurements and instrumental uncertainties are generally
assumed to be distributed according to this probability distribution.

It is
a continuous, symmetric distribution:

where
P(r) is the probability of a value r, µ is the expectation value
(mean) and s is the
standard deviation.

Vary
the values of m and s
to see the effect on distribution.

s corresponds to half the peak width at about 60% of full height.
Often, the full width at half maximum FWHM
is quoted.

FWHM
= @
2.35s.

The
peak value P(m) = .
Height of the curve at r =
m ± s: P(m ± s)
= .

target
practice is an example of the Gaussian distribution in two
dimensions.