# Math Help - Finding an unbiased estimator

1. ## Finding an unbiased estimator

Let $f(x; \theta) = \theta^x (1- \theta)$. I need to find an unbiased estimator for theta.

$E(X) = \Sigma x \theta^x (1- \theta) = (1-\theta)\Sigma x \theta^x = (1-\theta) \frac{\theta}{(1-\theta)^2} = \frac{\theta}{1 - \theta}$.

Kinda stuck here. I tried to find $E(\frac{1}{X})$, but that didn't help either.

Any help would be appreciated.

2. once again what is the support in this density?

3. Sorry about that. The support of X is 0, 1, 2,...,n and $0<= \theta < = 1$

I was able to use the taylor expansion -
but kinda got stuck there.

EDIT: Figured it out. Sorry for bothering you.