ProbabilityFunction - Maple Help

Statistics

 ProbabilityFunction
 compute the probability function

 Calling Sequence ProbabilityFunction(X, t, options)

Parameters

 X - algebraic; random variable or distribution t - algebraic; point (assumed to be an integer) options - (optional) equation of the form numeric=value; specifies options for computing the probability function of a random variable

Description

 • The ProbabilityFunction function computes the probability function of the specified discrete random variable at the specified point.
 • The first parameter can be either a discrete distribution (see Statistics[Distribution]) or a discrete random variable

Computation

 • By default, all computations involving random variables are performed symbolically (see option numeric below).
 • For more information about computation in the Statistics package, see the Statistics[Computation] help page.
 • For more information about computation in the Statistics package, see the Statistics[Computation] help page.

Options

 The options argument can contain one or more of the options shown below. More information for some options is available in the Statistics[RandomVariables] help page.
 • numeric=truefalse -- By default, the probability function is computed using exact arithmetic. To compute the probability function numerically, specify the numeric or numeric = true option.
 • mainbranch - returns the main branch of the distribution only.

Examples

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

Compute the probability function of the Geometric distribution with parameters p and q.

 > $\mathrm{ProbabilityFunction}\left(\mathrm{Geometric}\left(\frac{1}{3}\right),i\right)$
 $\left\{\begin{array}{cc}{0}& {i}{<}{0}\\ \frac{{\left(\frac{{2}}{{3}}\right)}^{{i}}}{{3}}& {\mathrm{otherwise}}\end{array}\right\$ (1)

Use numeric parameters.

 > $\mathrm{ProbabilityFunction}\left(\mathrm{Geometric}\left(\frac{1}{3}\right),5\right)$
 $\frac{{32}}{{729}}$ (2)
 > $\mathrm{ProbabilityFunction}\left(\mathrm{Geometric}\left(\frac{1}{3}\right),5,\mathrm{numeric}\right)$
 ${0.04389574760}$ (3)

References

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