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Help with Unbiased Estimators

  1. Nov 30, 2009 #1
    1. The problem statement, all variables and given/known data

    See attached.

    2. Relevant equations

    3. The attempt at a solution

    I have no issues with part A. I simply took the expected value of T1 and T2 and everything turned out fine. What I'm having issues with is part B.

    I have:
    T1 = (4 / n) * 1997 - 2 = 0.08075
    T2 = (4 / n) * 32 = 0.03334

    Why are my answers so different if they are both unbiased estimators? Shouldn't they at least be somewhat close to each other?
     

    Attached Files:

  2. jcsd
  3. Nov 30, 2009 #2
    Your answers are correct. The expected value of T1 is θ. However, any observed value of T1 may or may not be close to θ.
     
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