The probability table distribution is a discrete probability distribution with probability function given by:

subject to the following conditions, where $n$ is defined as the number of indices in plist:

The probability table distribution is defined by the sequence of integer variates 1..$n$. This distribution wrapper allows bounded discrete distributions to be easily represented in tabular form. If you would like to use a distribution that has values other than positive integers, consider using the EmpiricalDistribution, potentially with the probabilities option.

Note that the ProbabilityTable command is inert and should be used in combination with the RandomVariable command.

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

$P≔\left[\frac{1}{2}\,\frac{1}{4}\,\frac{1}{8}\,\frac{1}{16}\,\frac{1}{16}\right]$

$P≔\left[\frac{1}{2}\,\frac{1}{4}\,\frac{1}{8}\,\frac{1}{16}\,\frac{1}{16}\right]$

$X≔\mathrm{RandomVariable}\left(\mathrm{ProbabilityTable}\left(P\right)\right)\:$

$\mathrm{ProbabilityFunction}\left(X\,1\right)$

$\frac{1}{2}$

$\mathrm{CDF}\left(X\,2\right)$

$\frac{3}{4}$

$\mathrm{Sample}\left(X\,1000\right)$

Evans, Merran; Hastings, Nicholas; and Peacock, Brian. Statistical Distributions. 3rd ed. Hoboken: Wiley, 2000.

Johnson, Norman L.; Kotz, Samuel; and Balakrishnan, N. Continuous Univariate Distributions. 2nd ed. 2 vols. Hoboken: Wiley, 1995.

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