Let $X$ be negative binomial distributed with parameter $p$ and $r$.
Show that:
$1$) $E$($X$) = $r$ $\cdot$ $\frac{q}{p}$
$2$) $Var$($X$) = $r$ $\cdot$ $\frac{q}{q^2}$
$3$) Calculate the third central moment. So I have to calculate $E$(($X$ - $E$($X$))${^3}$).
I was able to calculate $1$) and $2$). But I have no idea how to calculate $3$).