Editing Probability-generating function (section)

=== Univariate case ===
If ''X'' is a [[discrete random variable]] taking values ''x'' in the non-negative [[integer]]s {0,1, ...}, then the ''probability generating function'' of ''X'' is defined as
<ref>{{ cite book | title = Probability and Distribution Theory | author = Gleb Gribakin | url = https://www.am.qub.ac.uk/users/g.gribakin/sor/Chap3.pdf }}</ref>

<math display="block">G(z) = \operatorname{E} (z^X) = \sum_{x=0}^{\infty} p(x) z^x,</math>
where <math>p</math> is the [[probability mass function]] of <math>X</math>.  Note that the subscripted notations <math>G_X</math> and <math>p_X</math> are often used to emphasize that these pertain to a particular random variable <math>X</math>, and to its [[Probability distribution|distribution]]. The power series [[absolute convergence|converges absolutely]] at least for all [[complex number]]s <math>z</math> with <math>|z|<1</math>; the radius of convergence being often larger.