Encyclopedia of Operations Research and Management Science

2013 Edition
| Editors: Saul I. Gass, Michael C. Fu

Probability Generating Function

Reference work entry
DOI: https://doi.org/10.1007/978-1-4419-1153-7_200642

For a non-negative integer-valued random variable X with probability mass function pj = Pr{X = j}, the probability generating function (often just called the generating function, and known in other fields as the z-transform) is given by \( P(z)=E[{z^X}]=\sum\limits_{j=0}^{\infty } {{z^j}{p_j}}. \)

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© Springer Science+Business Media New York 2013