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Math Help - Bias

  1. #1
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    Bias

    Suppose that X1, X2,...Xn is a random sample size n from a normal distribution
    N(0, theta) with mean 0 and variance theta.

    State which of these estimators, theta 1, 2 and 3 are biased, giving the bias if so. If not then give a justification

    theta 1 = \sum \frac{X^2}{(n-1)}
    theta 2 = \sum \frac{X^2}{n}
    theta 3 = nXbar^2

    Please just help me with a way into this question, a starting point, since I am clueless. A method to approach it and I will do all calculations. I know what a bias is but I don't know how to approach it. Find the real variance and equate? I am not sure. Thanks
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  2. #2
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    Re: Bias

    any ideas?
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  3. #3
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    Re: Bias

    In the first part, for example, you simply need to find the expected value of
    \sum \frac{X^2}{n-1}.

    Hint: You might find knowledge of the chi squared distribution useful (although that's not the only way).
    Last edited by awkward; December 1st 2011 at 05:15 PM.
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