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\begin{document}
$X$ is a \emph{negative binomial random variable} with parameters $r$ and $p$ if\\
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$f_X(x) ={r+x-1 \choose x} p^r (1-p)^x$,     $x=\{0,1,...\}$	\\
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Parameters:\\
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\begin{list}{$\star$ }{}
\item $r > 0$
\item $p \in [0,1]$
\end{list}
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Syntax:\\
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$X\sim NegBin(r,p)$\\
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Notes:\\
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\begin{enumerate}

\item If $r \in \mathbb{N}$, $X$ represents the number of failed Bernoulli trials before the $r$th success. Note that if $r=1$ the variable is a geometric random variable.
\item $E[X] = r \frac{1-p}{p}$
\item $Var[X] = r \frac{1-p}{p^2}$
\item $M_X(t) = (\frac{p}{1 - (1-p)e^t})^r$

\end{enumerate}
\end{document}
