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Math Help - Estimator Unbiased?

  1. #1
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    Estimator Unbiased?

    A sample of size 1 is drawn from the uniform pdf defined over the interval [0, \theta]. Find an unbiased estimator for \theta^2.

    Hint: Is \hat{\theta} = Y^2 unbiased?

    The uniform pdf is the function 1/ \theta correct? But then how does this translate to finding the unbiased estimator for \theta^2?
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  2. #2
    MHF Contributor matheagle's Avatar
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    Obtain the expected value of Y^2 and see.

    E(Y^2)= {1\over \theta}\int_0^{\theta}y^2dy={\theta^2\over 3}

    So 3Y^2 is unbiased for \theta^2
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