The Student:-Statistics subpackage represents distributions by random variables that follow that distribution.

Commands in this section are of the general form NameRandomVariable(arguments) where Name is the name of a distribution and arguments are the parameters for that distribution. For example, NormalRandomVariable(1,2) is a random variable distributed as $\mathrm{Normal}\left(1\,2\right)$ and PoissonRandomVariable(a) is a random variable distributed as $\mathrm{Poisson}\left(a\right)$.

Random variable commands available in Student:-Statistics subpackage are:

The command Sample can be used to generate a data sample which will follow the specified distribution and with the specified sample size.

$\mathrm{with}\left(\mathrm{Student}:-\mathrm{Statistics}\right)\:$

$A≔\mathrm{BinomialRandomVariable}\left(6\,\frac{1}{4}\right)\:$

$\mathrm{ProbabilityFunction}\left(A\,x\,\mathrm{output}=\mathrm{plot}\right)$

$\mathrm{StandardDeviation}\left(A\right)$

$\frac{3\sqrt{2}}{4}$

$\mathrm{Mean}\left(A\right)$

$\frac{3}{2}$

$B≔\mathrm{ExponentialRandomVariable}\left(3\right)\:$

$\mathrm{ProbabilityDensityFunction}\left(B\,x\right)$

$\left\{\begin{array}{cc}0& x<0\\ \frac{{\&ExponentialE;}^{-\frac{x}{3}}}{3}& \mathrm{otherwise}\end{array}\right.$

$\mathrm{CDF}\left(B\&comma;x\&comma;\mathrm{output}=\mathrm{plot}\right)$

$\mathrm{Variance}\left(B\right)$

$9$

$C≔2A+B\&colon;$

$\mathrm{Kurtosis}\left(C\right)$

$\frac{458}{81}$

$\mathrm{Skewness}\left(C\right)$

$\frac{13\sqrt{6}}{27}$

$\mathrm{Sample}\left(C\&comma;1000\right)$