 Integer-valued random variable

A random variable whose values lie in the integers with probability one. Its probability mass function is $p(j)=\mathbb{P}(X=j)$ for $j\in \mathbb{Z}$. If it is nonnegative, its probability generating function is $G(s)={\sum }_{j\ge 0}p(j)s^j$ wherever this expectation is finite.