Editing Probability-generating function (section)

{{Short description|Power series derived from a discrete probability distribution}}
In [[probability theory]], the '''probability generating function''' of a [[discrete random variable]] is a [[power series]] representation (the [[generating function]]) of the [[probability mass function]] of the [[random variable]].  Probability generating functions are often employed for their succinct description of the sequence of probabilities Pr(''X'' = ''i'') in the [[probability mass function]] for a [[random variable]] ''X'', and to make available the well-developed theory of power series with non-negative coefficients.