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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.

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

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

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

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

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

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

$\frac{3}{2}$

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

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

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

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

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

$9$

$C≔2A+B\&colon;$

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

$\frac{458}{81}$

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

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

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

$\left[2.48466998353152\&comma;7.77439725974354\&comma;4.78275800712335\&comma;2.64227075130962\&comma;11.0453426065179\&comma;2.74652026502560\&comma;8.06472380269561\&comma;13.6631975290842\&comma;5.56352252253889\&comma;2.58110649021619\&comma;2.27016972112320\&comma;0.976800565609142\&comma;6.13594738918389\&comma;4.95150398037618\&comma;0.180725358009541\&comma;2.62584025854149\&comma;7.07380613670492\&comma;3.08271795182814\&comma;6.18063261379935\&comma;4.33223593858277\&comma;6.81222428426989\&comma;0.289149268542139\&comma;17.3264117960489\&comma;6.83706093647346\&comma;4.99520346066036\&comma;2.41363989843860\&comma;8.98732861057565\&comma;7.48913448365461\&comma;0.0469552823869628\&comma;5.55125244438150\&comma;4.58150846343969\&comma;3.88650803499280\&comma;2.83043299279514\&comma;3.07806778754470\&comma;3.17140397169609\&comma;9.93168049975396\&comma;6.67257275985396\&comma;4.15782797300241\&comma;6.97326753517901\&comma;4.47362113186557\&comma;1.54666908133360\&comma;6.69163957130109\&comma;2.07945978534720\&comma;2.04745199525005\&comma;3.28763177963972\&comma;4.96667134775745\&comma;3.81345387191222\&comma;5.03084264942554\&comma;6.14078314094173\&comma;5.94966745296547\&comma;1.40903432814941\&comma;7.05437368167844\&comma;6.23723040219234\&comma;10.6513990341751\&comma;2.53444236442640\&comma;6.07877827157173\&comma;9.95985276436900\&comma;6.36246873936350\&comma;3.90942296673929\&comma;7.09878826057811\&comma;6.69471067774276\&comma;3.49355672949018\&comma;0.661509717591572\&comma;5.81390950611851\&comma;1.13451739252842\&comma;7.63902474796554\&comma;3.19655990868765\&comma;1.39291537729941\&comma;0.0578418548076576\&comma;6.51703552083120\&comma;12.3484443183855\&comma;10.0568432993359\&comma;2.44916127233082\&comma;11.3536423380737\&comma;9.18293281545800\&comma;3.48727323726787\&comma;2.62007043159306\&comma;2.71480903625125\&comma;7.00660533981913\&comma;1.07362568991261\&comma;5.46878494889028\&comma;0.731371469739179\&comma;0.781303973562075\&comma;5.17984897261302\&comma;4.93044029549323\&comma;4.64944853673596\&comma;9.43454082856064\&comma;4.85733694910028\&comma;6.59899558292129\&comma;4.94237564944424\&comma;6.22605076497462\&comma;3.60411541311169\&comma;9.71044837917128\&comma;3.51817878157215\&comma;6.56881208350422\&comma;4.72961181374425\&comma;4.02149775564965\&comma;9.67008620670676\&comma;11.9687563898451\&comma;8.32583873832573\&comma;\dots \&comma;\text{⋯ 900 row vector entries not shown}\right]$