I have a question about the negative binomial distribution. Say, $P(X=x)= \dbinom{x-1}{M-1} p^M (1-p)^{x-M}$. I already found that $\hat{p}=\dfrac{M - 1}{X - 1}$ is an unbiased estimator, but I got stuck while trying to find $\operatorname{Var}(\hat{p})$. Can anyone help me with that?
Thanks!