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Math Help - Unbiased Estimator

  1. #1
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    Unbiased Estimator

    I have a question on unbiased estimators and im completely lost...
    please help!
    Attached Thumbnails Attached Thumbnails Unbiased Estimator-screen-shot-2009-12-01-14.00.34.png  
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  2. #2
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    What value of c would satisfy the following:

    E(c(X_1 + 2X_2)) = \frac{1}{\theta}
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  3. #3
    MHF Contributor matheagle's Avatar
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    Quote Originally Posted by statmajor View Post
    What value of c would satisfy the following:

    E(c(X_1 + 2X_2)) = \frac{1}{\theta}
    since they are i.i.d.

    3cE(X) = \frac{1}{\theta}
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  4. #4
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    Quote Originally Posted by matheagle View Post
    since they are i.i.d.

    [tex]3cE(X) = \frac{1}{\theta}[/m
    ath]
    Sorry but can you explain what you just did? And what is I.I.d?
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  5. #5
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    Quote Originally Posted by jmat View Post
    Sorry but can you explain what you just did? And what is I.I.d?
    It means independent and identically distributed. From which it follows that E(X1) = E(X2). From which matheagle's equation follows. And you should know how to calculate an expected value when you have the pdf.
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