---
tag: 0EBCWQ8BVE
kind: concept
name: Probability-generating function
aliases: [probability-generating-function, pgf]
msc: ["60E05"]
sources:
  - url: https://en.wikipedia.org/wiki/Probability_generating_function
    locator: lead section
same_as:
  wikidata: Q372071
  wikipedia: Probability generating function
---

## Summary

The probability-generating function of a random variable with values in $\{0, 1, 2, \dots\}$ is the power series whose coefficients are the probabilities $P(X = k)$.
The node [[probability-generating function|0Z8PSSAVBA]] gives the precise definition.