Gaussian Distribution

The Gaussian distribution is often called the normal distribution . It is given by:


The constant, determines the width of the distribution, and is known as the standard deviation. The mean value of x is

and the mean square value of x is

The root mean square deviation and the standard deviation are the same (i.e. ). The probable error pe is defined as a value of x such that the probability of x lying inside (or outside) of pe is . (pe = 0.67 .)

In many experimental situations the Gaussian distribution describes the deviations of repeated measurements from the mean. It has the characteristics that positive and negative deviations are equally likely, and small deviations are much more likely than large deviatoins. The distributoin of successive counts from counter tubes is not symmetric about the mean, since negative counts do not occur, and some other distribution function must be used in the statistical analysis of counting data.

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