# Homework Help: Finding an Unbiased estimator

1. Mar 23, 2010

### cse63146

1. The problem statement, all variables and given/known data

Find an unbiased etimator for theta with PDF $$f(x; \theta) = \theta^x (1- \theta)$$. The support of x = 0,1,2,3,....

2. Relevant equations

3. The attempt at a solution

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

$$E(1+x) = \frac{1}{1- \theta}$$. Now I'm stuck here.

Any help would be greately appreciated.