\begin{definition}[Definition:Negative Binomial Distribution/First Form]
Let $X$ be a discrete random variable on a probability space $\struct {\Omega, \Sigma, \Pr}$.
$X$ has the '''negative binomial distribution (of the first form) with parameters $n$ and $p$''' if:
:$\Img X = \set {0, 1, 2, \ldots}$
:$\map \Pr {X = k} = \dbinom {n + k - 1} {n - 1} p^k \paren {1 - p}^n$
where $0 < p < 1$.
It is frequently seen as:
:$\map \Pr {X = k} = \dbinom {n + k - 1} {n - 1} p^k q^n$
where $q = 1 - p$.
\end{definition}