I have a bernoulli RV $X$ defined as below:
$pr(X=1)=1-(1-p)^{k}$
$pr(X=0)=(1-p)^{k}$
Assume I have $N$ independent observations on the RV $X$. I am interested in finding the MLE estimator of $k$ and its variance.
My attempt: let $\mu=1-(1-p)^{k}$ . Then, $\hat{\mu}=\frac{\sum{x_i}}{N}$. Thus, $\hat{k}=\frac{log(1-\frac{\sum{x_i}}{N})}{log(1-p)}$. But, I am not sure what is the best approach to find the variance of $\hat{k}$.Can someone guide me through those steps?