Finding an unbiased estimator

**statmajor** · March 22nd 2010, 01:19 PM

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.

**matheagle** · March 22nd 2010, 01:58 PM

once again what is the support in this density?

**statmajor** · March 23rd 2010, 06:39 AM

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.

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