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Estimator question

  1. Apr 5, 2005 #1
    ok, so we know that an estimator for 1/theta, for 0<y<theta is (theta hat) = 2/n * sum from 1 to n of Y(i).

    to prove that the estimator is unbiased, I need to show that the expected value of (theta hat) = theta.

    so E(2/n*sum from 1 to n of Y(i)) =

    2/n * sum from 1 to n of E(Y(i)).

    then the book says we can cancel stuff because E(Y(i)) = theta/2.

    so why is it equal to theta/2? I'm doing other problems simlar to this, so do I just put E(Y(i)) = theta/2 for everything?

  2. jcsd
  3. Apr 6, 2005 #2
    I think that E(y) is equal to y/2 ONLY if the distribution of y is uniform.

    Think about a flat probability distribution function in y from 0 to 1. The expected value of y is 1/2.

    You also mentioned that the estimator is for 1/theta, not theta, which doesn't seem consistent since you're referring to theta^hat.
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