The negative binomial probability mass function is [ begin{aligned} & qquad f(y, pi, alpha)=left(begin{array}{c} y+alpha-1 alpha-1 end{array} ight) pi^{alpha}(1-pi)^{y} & text { for

The negative binomial probability mass function is

\[
\begin{aligned}
& \qquad f(y, \pi, \alpha)=\left(\begin{array}{c}
y+\alpha-1 \\
\alpha-1
\end{array}\right) \pi^{\alpha}(1-\pi)^{y} \\
& \text { for } y=0,1,2, \ldots, \alpha>0 \text { and } 0 \leq \pi \leq 1
\end{aligned}
\]

Show that the negative binomial is a member of the exponential family.