Category:Definitions/Probability Generating Functions

This category contains definitions related to Probability Generating Functions.
Related results can be found in Category:Probability Generating Functions.

Let $X$ be a discrete random variable whose codomain, $\Omega_X$, is a subset of the natural numbers $\N$.

Let $p_X$ be the probability mass function for $X$.

The probability generating function for $X$, denoted $\map {\Pi_X} s$, is the formal power series defined by:

$\ds \map {\Pi_X} s := \sum_{n \mathop = 0}^\infty \map {p_X} n s^n \in \R \sqbrk {\sqbrk s}$