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Math Help - Finding E(X) and V(X) of a Max function

  1. #1
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    Finding E(X) and V(X) of a Max function

    Hey guys,
    So I have X_{1},...,X_{n} ~ Uniform ( 0, \theta) where \hat\theta=max{ X_{1},...,X_{n}} .
    All I have to do is find Bias and se.
    How Do I find the Bias and se?
    Bias=E( \hat\theta)- \theta
    How Do I find expected value and \theta?
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  2. #2
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    Re: Finding E(X) and V(X) of a Max function

    Hey farmeruser1.

    Do you have the distribution of the order statistic of the uniform distributions (the maximum)? (This will help solve all the problems in this question).
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  3. #3
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    Re: Finding E(X) and V(X) of a Max function

    Hey chiro,
    Looking at Wikipedia, It says E( X_{k})= k/(n+1)
    So How would I find the Biad?
    Bias=E( n/(n+1)+ \theta?
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  4. #4
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    Re: Finding E(X) and V(X) of a Max function

    What is the distribution of the order statistic (maximum)? You need this in order to proceed (especially for the variance of the estimator).

    Your bias is calculated as E[theta_hat] - theta.
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