Poisson random variable - Maple Help

Home : Support : Online Help : Education : Student Package : Statistics : Random Variable Distributions : Student/Statistics/PoissonRandomVariable

Student[Statistics][PoissonRandomVariable] - Poisson random variable

 Calling Sequence PoissonRandomVariable(lambda)

Parameters

 lambda - intensity parameter

Description

 • The Poisson random variable is a discrete probability random variable with probability function given by:

$f\left(t\right)=\left\{\begin{array}{cc}0& t<0\\ \frac{{\mathrm{\lambda }}^{t}{ⅇ}^{-\mathrm{\lambda }}}{t!}& \mathrm{otherwise}\end{array}\right\$

 subject to the following conditions:

$0<\mathrm{\lambda }$

Notes

 • The Quantile and CDF functions applied to a Poisson random variable use a sequence of iterations in order to converge upon the desired output point.  The maximum number of iterations to perform is equal to 100 by default, but this value can be changed by setting the environment variable _EnvStatisticsIterations to the desired number of iterations.

Examples

 > $\mathrm{with}\left(\mathrm{Student}[\mathrm{Statistics}]\right):$
 > $X:=\mathrm{PoissonRandomVariable}\left(\mathrm{λ}\right):$
 > $\mathrm{ProbabilityFunction}\left(X,u\right)$
 ${{}\begin{array}{cc}{0}& {u}{<}{0}\\ \frac{{{\mathrm{λ}}}^{{u}}{}{{ⅇ}}^{{-}{\mathrm{λ}}}}{{u}{!}}& {\mathrm{otherwise}}\end{array}$ (1)
 > $\mathrm{ProbabilityFunction}\left(X,2\right)$
 $\frac{{1}}{{2}}{}{{\mathrm{λ}}}^{{2}}{}{{ⅇ}}^{{-}{\mathrm{λ}}}$ (2)
 > $\mathrm{Mean}\left(X\right)$
 ${\mathrm{λ}}$ (3)
 > $\mathrm{Variance}\left(X\right)$
 ${\mathrm{λ}}$ (4)
 > $Y:=\mathrm{PoissonRandomVariable}\left(3\right):$
 > $\mathrm{ProbabilityFunction}\left(Y,x,\mathrm{output}=\mathrm{plot}\right)$
 > $\mathrm{CumulativeDistributionFunction}\left(Y,x,\mathrm{output}=\mathrm{plot}\right)$