The RandomVariable command creates new random variable with the specified distribution.

The parameter can be one of the supported distributions or a distribution data structure.

with(Statistics):

X := RandomVariable(Normal(a, b));

$X≔\mathrm{\_R}$

PDF(X, t);

$\frac{\sqrt{2}{\ⅇ}^{-\frac{{\left(t-a\right)}^2}{2b^2}}}{2\sqrt{\mathrm{\pi }}b}$

Mean(X);

$a$

T := Distribution(GammaDistribution(u, v));

$T:=\mathbf{module}\left(\right)\mathbf{option}\mathrm{Distribution}\,\mathrm{Continuous}\;\mathbf{export}\mathrm{Conditions}\,\mathrm{ParentName}\,\mathrm{Parameters}\,\mathrm{CharacteristicFunction}\,\mathrm{CGF}\,\mathrm{Mean}\,\mathrm{Mode}\,\mathrm{MGF}\,\mathrm{PDF}\,\mathrm{Support}\,\mathrm{Variance}\,\mathrm{CDFNumeric}\,\mathrm{QuantileNumeric}\,\mathrm{RandomSample}\,\mathrm{RandomSampleSetup}\,\mathrm{RandomVariate}\,\mathrm{MaximumLikelihoodEstimate}\;\mathbf{end\; module}$

Y := RandomVariable(T);

$Y≔\mathrm{\_R0}$

PDF(Y, t);

$\left\{\begin{array}{cc}0& t<0\\ \frac{{\left(\frac{t}{u}\right)}^{v-1}{\&ExponentialE;}^{-\frac{t}{u}}}{u\mathrm{\Gamma }\left(v\right)}& \mathrm{otherwise}\end{array}\right.$

U := Distribution(PDF = (t -> piecewise(t < 0, 0, t < 3, 1/3, 0)));

$U:=\mathbf{module}\left(\right)\mathbf{option}\mathrm{Distribution}\&comma;\mathrm{Continuous}\&semi;\mathbf{export}\mathrm{PDF}\&comma;\mathrm{Conditions}\&semi;\mathbf{end\; module}$

Z := RandomVariable(U);

$Z≔\mathrm{\_R1}$

PDF(Z, t);

$\left\{\begin{array}{cc}0& t<0\\ \frac{1}{3}& t<3\\ 0& \mathrm{otherwise}\end{array}\right.$

Mean(Z);

$\frac{3}{2}$

Stuart, Alan, and Ord, Keith. Kendall's Advanced Theory of Statistics. 6th ed. London: Edward Arnold, 1998. Vol. 1: Distribution Theory.