Corollary 7.5.7. Negative Binomial Properties via Moment Generating Function.
\begin{equation*}
M(0) = 1
\end{equation*}
\begin{equation*}
M'(0) = \frac{r}{p}
\end{equation*}
\begin{equation*}
M''(0) = \left ( \frac{r(1-p)}{p^2} \right )^2 + \left ( \frac{r}{p} \right )^2
\end{equation*}