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Gaussian distribution
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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, 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.

The significance of the area under the Gaussian distribution should also be analysed.

 

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1999, 2000 The University of Liverpool, Department of Physics

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