# Symbols:Greek/Pi/Probability Generating Function

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## Probability Generating Function

$\map {\Pi_X} s$

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:

$\displaystyle \map {\Pi_X} s := \sum_{n \mathop = 0}^\infty \map {p_X} n s^n \in \R \left[\left[{s}\right]\right]$

The $\LaTeX$ code for $\map {\Pi_X} s$ is \map {\Pi_X} s .