Integer-valued random variable
= Integer-valued random variable
{title2=$\mathbb P(X\in\mathbb Z)=1$}
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 $G(s)=\sum_{j\ge0}p(j)s^j$ wherever this <expectation> is finite.