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Math Help - Unbiased Estimator

  1. #1
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    Unbiased Estimator

    X1,...Xn~N(mu,sigma^2)
    (sigma^2 known)

    is the estimator mu=(average(x))^2-((sigma^2)/n)
    an unbiased estimator to mu^2 ?

    cheers
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  2. #2
    MHF Contributor matheagle's Avatar
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    yes, since sigma is known
    AND normality has nothing to do with this
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  3. #3
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    why is it unbiased, how did you work it out ?
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  4. #4
    MHF Contributor matheagle's Avatar
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     E(\bar X^2) =V(\bar X) + (E\bar X)^2={\sigma^2\over n}+\mu^2
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  5. #5
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    just one question if I might:

    an estimator T is unbiased if E(T)=parameter

    where in the solution we calculated E(T) ?
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