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Math Help - variance unbiased estimator

  1. #1
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    variance unbiased estimator

    Show that the mean of a random sample of size n is a minimum variance unbiased estimator of "lambda", of a Poisson distribution.

    Can anybody provide some help for me?
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  2. #2
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    You'll need to use the Lehmann–Scheffé theorem which states that if Y is a complete sufficient statistic for lambda, and there exists a function of Y such that this function is an unbiased estimator of lambda, then this function is an MVUE of lambda.

    1. Find a complete sufficient statistic (Y) for lambda
    2. Find a function of Y such that this function is an unbiased estimator of lambda.
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  3. #3
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    Can somebody give me some more detailed advice? I am still having trouble with this
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  4. #4
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    Fine. Here's a hint: The complete sufficient statistic for a poisson distribution is \Sigma^n_1 X_i = n \overline{X}. What's the expecation of \Sigma^n_1 X_i?
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