$\displaystyle f(x|\theta) = \left(\begin{array}{c}x-1\\m-1\end{array}\right)\theta^m(1-\theta)^{x-m}$ x = m, m+1, etc... and m>=2

I find the mle of $\displaystyle \theta = \frac{m}{x}$, so good so far...

The next part is to find a constant $\displaystyle a$ s.t.

$\displaystyle \tilda{\theta(X)} \equiv \frac{a}{X-1} $ is an unbiased estimator of $\displaystyle \theta$

I could just plug in the mle estimator to a and use that, but that doesn't feel correct.

Thanks!