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

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.

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.

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

$\mathrm{ProbabilityFunction}\left(\mathrm{Geometric}\left(\frac{1}{3}\right)\,i\right)$

$\left\{\begin{array}{cc}0& i<0\\ \frac{{\left(\frac{2}{3}\right)}^i}{3}& \mathrm{otherwise}\end{array}\right.$

$\mathrm{ProbabilityFunction}\left(\mathrm{Geometric}\left(\frac{1}{3}\right)\&comma;5\right)$

$\frac{32}{729}$

$\mathrm{ProbabilityFunction}\left(\mathrm{Geometric}\left(\frac{1}{3}\right)\&comma;5\&comma;\mathrm{numeric}\right)$

$0.04389574760$

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