Normal Probability Distributions

The standard normal distribution, in Maple, is

> ND := (mu,sigma,x) -> 1/sqrt(2*Pi*sigma^2)*exp(-1/2*((x-mu)/sigma)^2);

ND := proc (mu, sigma, x) options operator, arrow; ...

We graph ND(1,s,x) with s varying from 0.5 up to 3.


Note how s affects the dispersion of the function. In statistics, this measure is called the standard deviation.
Below, we plot ND(m,1,x) with m varying from -5 to +5.


This variation can be explained as a horizontal translation. In statistics, m is called the mean.