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Math Help - Unbiased Estimator

  1. #1
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    Unbiased Estimator

    Could someone please help with the attached problem. Intuitively I would think that the answer is 1 but I don't know how to demonstrate it.
    Thanks for your help.
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  2. #2
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    Quote Originally Posted by Connemara Pony View Post
    Could someone please help with the attached problem. Intuitively I would think that the answer is 1 but I don't know how to demonstrate it.
    Thanks for your help.
    An unbiased estimator is one with expected value equal to that which is being estimated.

    E(\hat{\theta})=E(X_1+X_2+aX_3)=\theta+\theta+a\th  eta=(2+a)\theta

    So to make this an unbiased estimator we need a=-1

    RonL
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