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Math Help - Exponential Distribution Question

  1. #1
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    Exponential Distribution Question

    Let X be teh mean of a random sample from the exponential distribution Exp(\theta)

    Show that X is an unbiased point estimater of \theta

    Which PDF of the exponential function do I use?

    or
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  2. #2
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    The sample mean is an unbiased estimator for the true mean. For which of those distributional forms is the defining parameter the mean? That should give you the answer.
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  3. #3
    MHF Contributor matheagle's Avatar
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    IF X_1,X_2,... are iid then

    E(\bar X)=\mu which is \theta in this case

    or \lambda or \beta
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  4. #4
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    Quote Originally Posted by matheagle View Post
    IF X_1,X_2,... are iid then

    E(\bar X)=\mu which is \theta in this case

    or \lambda or \beta
    That part I got I wasnt sure which one of the PDF I needed to use, since the one with lambda's expectation is 1/lambda (according to wikipedia)
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  5. #5
    MHF Contributor matheagle's Avatar
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    They are the same, \lambda=1/\beta use whatever your book is using.
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  6. #6
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    That clears that up. Thanks.
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