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Math Help - Unbiased

  1. #1
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    Unbiased

    i tried very hard to solve this question but i really can't. If someone can please help me? Please????
    Thank you
    Maria
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  2. #2
    MHF Contributor matheagle's Avatar
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    you can prove that E(S^2)=\sigma^2 but you cannot pull the square root through the expectation.

    I would just cook up an example and show that E(S)\ne \sigma

    Try a bernoulli with P(X=0)=1-p and P(X=1)=p.
    Here you have pq as the pop. variance.
    Let n=3 and obtain the distribution of S and see what happens.

    The sample of (0,0,0) occurs with probability q times q times q.
    A sample of two 0's and one 1 occurs with probability pqq, but there are 3 of those....
    So you can derive the distribution of S via these four possibilities.
    Last edited by matheagle; November 25th 2009 at 05:17 PM.
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  3. #3
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    Can you please show me how cause i can't understand?
    Thank you
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  4. #4
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    Quote Originally Posted by maria69 View Post
    Can you please show me how cause i can't understand?
    Thank you
    Please show some effort after getting help. What have you done and where do you get stuck?
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