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Math Help - minimum variance unbiased estimators

  1. #1
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    minimum variance unbiased estimators

    Show that the sample proportion (X/n) is a minimum variance unbiased estimator of the binomial parameter theta. The hint that is given is to treat (X/n) as the mean of a random sample of size n from a Bernoulli population with the parameter theta.

    So, I know that I have to use the Cramer-Rao inequality. And I also know the distribution of Bernoulli, which is f(x; theta) = (theta^x)((1-theta)^(1-x)). I took the natural log of this and the partial derivative but I don't know what to do with the expected value of it. Can anyone help me?
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  2. #2
    MHF Contributor matheagle's Avatar
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    You need to understand X and the sample of Xi's
    It might be clearer if you use Y instead of X
    The distribution of each Xi is

    f(x_i) = \theta^{x_i}(1-\theta)^{1-x_i}

    Next take the product of these, for your likelihood function and

    let Y=\sum_{i=1}^nX_i
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