This can be illustrated as
where m is the mean of the random variable and s is the standard deviation of the random variable.
and can be illustrated as
The cumulative distribution function (CDF) of an Gaussian random variable is not available in a closed form, because the pdf equation is not integrable. Instead tables are used to find the value of this function at several values.
The tables come in three common forms and innumerable less common forms. Each is the numerical integration of the unit normal (N[0,1]) gaussian pdf but integrated over different regions.
is the proper CDF of the Gaussian:
erf(x) is the integral from 0 to x:
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