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Math Help - Finding an unbiased estimator

  1. #1
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    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.
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  2. #2
    MHF Contributor matheagle's Avatar
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    once again what is the support in this density?
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  3. #3
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    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.
    Last edited by statmajor; March 23rd 2010 at 03:28 PM.
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