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Math Help - Unbiasedness

  1. #1
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    Unbiasedness

    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 theta hat = Y^2 unbiased?
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  2. #2
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    Quote Originally Posted by eigenvector11 View Post
    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 theta hat = Y^2 unbiased?
    Use the hint!

    E(Y^2) = k \theta^2 therefore E\left( \frac{Y^2}{k}\right) = \theta^2 therefore \frac{Y^2}{k} is an unbiased estimator for \theta^2.

    I leave it to you to get the value of k by solving an appropriate integral.
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