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Math Help - Finding the Variance of (1/S)

  1. #1
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    Finding the Variance of (1/S)

    Given that we have X_{1}, ... , X_{n} \sim iid  G where G is unknown.

    Find V(\overline{X} / S) Where X is the sample Mean, S^2 is the sample variance and V( \cdot ) is the variance.
    So...
    V(\overline{X} / S) = E[\overline{X}^2 / S^2] - E[\overline{X} / S]^2
    Since \overline{X} and S^2 are independent,
    V(\overline{X} / S) = E[\overline{X}^2]E[1 / S^2] - E[\overline{X} / S]^2

    We were having a real hard time finding E[1 / S^2]. Also, can the E[\overline{X} / S]^2 be broken up in a similar way to the other term?

    Is there another way to approach this problem?
    Last edited by jameselmore91; November 6th 2011 at 09:08 AM. Reason: Fixing LaTex / Rewording problem.
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  2. #2
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    Re: Finding the Variance of (1/S)

    I can't get the LaTex to work. But the first error is the variance of the sample mean divided by the sample standard deviation. We've been haveing a hard time finding the E(1/S) and E(1/S^2)... Any ideas?
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  3. #3
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    Re: Finding the Variance of (1/S)

    Quote Originally Posted by jameselmore91 View Post
    We've been asked to find the  Var( \bar{X} / S) where \bar{X} is the Sample Mean and S is the Sample Variance.

    We've worked it all out but are having a hard time caclulating Var(1/S) and Var((1/S)^2).
    Any ideas? Is there an easier way to approach this problem?
    Use [TEX]...[/TEX] raps for LaTeX.
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    Re: Finding the Variance of (1/S)

    Without any further asumption on the rv's distributions, it's not possible to say anything...
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  5. #5
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    Re: Finding the Variance of (1/S)

    The only thing known about the random variables is that they are identically and independently distributed with population mean and variance "sigma squared"
    Last edited by jameselmore91; November 6th 2011 at 11:29 AM.
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