Random variables available in Student[Statistics] - Maple Programming Help

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Random variables available in Student[Statistics]

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{Student}\left[\mathrm{Statistics}\right]\right):$

Define a discrete distribution that follows $\mathrm{Binomial}\left(6,\frac{1}{4}\right)$

 > $A≔\mathrm{BinomialRandomVariable}\left(6,\frac{1}{4}\right):$
 > $\mathrm{ProbabilityFunction}\left(A,x,\mathrm{output}=\mathrm{plot}\right)$
 > $\mathrm{StandardDeviation}\left(A\right)$
 $\frac{{3}{}\sqrt{{2}}}{{4}}$ (1)
 > $\mathrm{Mean}\left(A\right)$
 $\frac{{3}}{{2}}$ (2)

Define a continuous distribution that follow $\mathrm{Exponential}\left(3\right)$

 > $B≔\mathrm{ExponentialRandomVariable}\left(3\right):$
 > $\mathrm{ProbabilityDensityFunction}\left(B,x\right)$
 $\left\{\begin{array}{cc}{0}& {x}{<}{0}\\ \frac{{{ⅇ}}^{{-}\frac{{x}}{{3}}}}{{3}}& {\mathrm{otherwise}}\end{array}\right\$ (3)
 > $\mathrm{CDF}\left(B,x,\mathrm{output}=\mathrm{plot}\right)$
 > $\mathrm{Variance}\left(B\right)$
 ${9}$ (4)

Define a distribution that follow $2\mathrm{Binomial}\left(6,\frac{1}{4}\right)+\mathrm{Exponential}\left(3\right)$

 > $C≔2A+B:$
 > $\mathrm{Kurtosis}\left(C\right)$
 $\frac{{458}}{{81}}$ (5)
 > $\mathrm{Skewness}\left(C\right)$
 $\frac{{13}{}\sqrt{{6}}}{{27}}$ (6)

We can also randomly generate a sample from this distribution with sample size equal to 1000.

 > $\mathrm{Sample}\left(C,1000\right)$
  (7)

Compatibility

 • The Random variables available in Student[Statistics] command was introduced in Maple 18.