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Finding an Unbiased estimator

  1. Mar 23, 2010 #1
    1. The problem statement, all variables and given/known data

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

    2. Relevant equations

    3. The attempt at a solution

    [tex]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}[/tex].

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

    Any help would be greately appreciated.
  2. jcsd
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