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    Maximum likelihood and Fisher information

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    Suppose x(sub 1), x(sub 2), ..., x(sub n) is a random sample from a distribution with probability density

    f(x/Î?)=( 1 / (Î?+1)) e^(-x/(Î?+1) where x>0 and Î?> -1

    A. Find the maximum likelihood estimator of Î? and show it is unbiased.
    B. Find the Fisher Information I(Î?).
    C. Does the variance of the maximum likelihood estimator attain the Cramer-Rao lower bound?

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    https://brainmass.com/statistics/maximum-likelihood-estimation/maximum-likelihood-fisher-information-315418

    Solution Summary

    Suppose x(sub 1), x(sub 2), ..., x(sub n) is a random sample from a distribution with probability density

    f(x/Î?)=( 1 / (Î?+1)) e^(-x/(Î?+1) where x>0 and Î?> -1

    A. Find the maximum likelihood estimator of Î? and show it is unbiased.

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