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 random variable, or a continuous random variable.

If the option inert is not included or is specified to be inert=false, then the function will return the actual value of the result. If inert or inert=true is specified, then the function will return the formula of evaluating the actual value.

By default, all computations involving random variables are performed symbolically (see option numeric below).

If the option numeric is included, then the computation is done in floating point. Otherwise the computation is exact.

If the first parameter is a continuous random variable, then the result is always 0.

By default, the probability function of the specified random variable at the specified point is computed according to the rules mentioned above. To always compute the value numerically, specify the numeric or numeric = true option.

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

$\mathrm{ProbabilityFunction}\left(\mathrm{BinomialRandomVariable}\left(n\,p\right)\,x\right)$

$\left\{\begin{array}{cc}0& x<0\\ \left(\genfrac{}{}{0ex}{}{n}{x}\right)p^x{\left(1-p\right)}^{n-x}& \mathrm{otherwise}\end{array}\right.$

$\mathrm{ProbabilityFunction}\left(\mathrm{BinomialRandomVariable}\left(10\&comma;\frac{1}{3}\right)\&comma;5\right)$

$\frac{896}{6561}$

$\mathrm{ProbabilityFunction}\left(\mathrm{BinomialRandomVariable}\left(10\&comma;\frac{1}{3}\right)\&comma;5\&comma;\mathrm{numeric}\right)$

$0.1365645480$

$\mathrm{ProbabilityFunction}\left(\mathrm{BinomialRandomVariable}\left(10\&comma;\frac{1}{3}\right)\&comma;5\&comma;\mathrm{output}=\mathrm{plot}\right)$

$\mathrm{ProbabilityFunction}\left(\mathrm{BetaRandomVariable}\left(2\&comma;3\right)\&comma;5\right)$

$0$

$\mathrm{ProbabilityFunction}\left(\mathrm{NormalRandomVariable}\left(8\&comma;5\right)\&comma;2\right)$

$0$

$X≔\mathrm{BinomialRandomVariable}\left(7\&comma;\frac{1}{2}\right)+\mathrm{NegativeBinomialRandomVariable}\left(3\&comma;\frac{1}{2}\right)\&colon;$

$\mathrm{ProbabilityFunction}\left(X\&comma;2\&comma;\mathrm{inert}\right)$

$\sum _{u_1=0}^{\mathrm{\infty }}\left(\left\{\begin{array}{cc}0& u_1<0\\ \frac{\left(\genfrac{}{}{0ex}{}{2+u_1}{u_1}\right){\left(\frac{1}{2}\right)}^{u_1}}{8}& \mathrm{otherwise}\end{array}\right.\right)\left(\left\{\begin{array}{cc}0& -u_1<\mathrm{-2}\\ \left(\genfrac{}{}{0ex}{}{7}{2-u_1}\right){\left(\frac{1}{2}\right)}^{2-u_1}{\left(\frac{1}{2}\right)}^{5+u_1}& \mathrm{otherwise}\end{array}\right.\right)$

$\mathrm{evalf}\left(\mathrm{ProbabilityFunction}\left(X\&comma;2\&comma;\mathrm{inert}\right)\right)$

$0.03222656250$

$\mathrm{ProbabilityFunction}\left(X\&comma;2\&comma;\mathrm{numeric}\right)$

$0.03222656250$

$\mathrm{probability},\mathrm{graph}≔\mathrm{ProbabilityFunction}\left(\mathrm{PoissonRandomVariable}\left(4\right)\&comma;7\&comma;\mathrm{output}=\mathrm{both}\right)\&colon;$

$\mathrm{probability}$

$\frac{1024{\&ExponentialE;}^{\mathrm{-4}}}{315}$

$\mathrm{graph}$

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

The Student[Statistics][ProbabilityFunction] command was introduced in Maple 18.

For more information on Maple 18 changes, see Updates in Maple 18.