normal (Gaussian) distribution - Maple Help

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Statistics[Distributions][Normal] - normal (Gaussian) distribution

 Calling Sequence Normal(mu, sigma) NormalDistribution(mu, sigma)

Parameters

 mu - distribution mean sigma - scale parameter

Description

 • The normal distribution is a continuous probability distribution with probability density function given by:

$f\left(t\right)=\frac{\sqrt{2}{ⅇ}^{-\frac{{\left(t-\mathrm{\mu }\right)}^{2}}{2{\mathrm{\sigma }}^{2}}}}{2\sqrt{\mathrm{\pi }}\mathrm{\sigma }}$

 subject to the following conditions:

$\mathrm{\mu }::\mathrm{real},0<\mathrm{\sigma }$

 • The normal variate Normal(mu,sigma) is related to the standardized variate Normal(0,1) by Normal(0,1) ~ (Normal(mu,sigma)-mu)/sigma.
 • Note that the Normal command is inert and should be used in combination with the RandomVariable command.

Examples

 > $\mathrm{with}\left(\mathrm{Statistics}\right):$
 > $X:=\mathrm{RandomVariable}\left(\mathrm{Normal}\left(\mathrm{μ},\mathrm{σ}\right)\right):$
 > $\mathrm{PDF}\left(X,u\right)$
 $\frac{{1}}{{2}}{}\frac{\sqrt{{2}}{}{{ⅇ}}^{{-}\frac{{1}}{{2}}{}\frac{{\left({u}{-}{\mathrm{μ}}\right)}^{{2}}}{{{\mathrm{σ}}}^{{2}}}}}{\sqrt{{\mathrm{π}}}{}{\mathrm{σ}}}$ (1)
 > $\mathrm{PDF}\left(X,0.5\right)$
 $\frac{{0.3989422802}{}{{ⅇ}}^{{-}\frac{{0.5000000000}{}{\left({0.5}{-}{1.}{}{\mathrm{μ}}\right)}^{{2}}}{{{\mathrm{σ}}}^{{2}}}}}{{\mathrm{σ}}}$ (2)
 > $\mathrm{Mean}\left(X\right)$
 ${\mathrm{μ}}$ (3)
 > $\mathrm{Variance}\left(X\right)$
 ${{\mathrm{σ}}}^{{2}}$ (4)