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