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Math Help - E(1/sn) and var(1/sn)

  1. #1
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    E(1/sn) and var(1/sn)

    Hi
    i have a question, when we have continuous variables, how we can calculate var (1/sn)
    can we always change summation and integral?

    for example x1,...,xn have G(a,b) distribution funcation... how we can calculate var (1/sn)?

    we know E(xi)=ab , var(xi)= ab^2

    Best wishes
    zayrsil
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  2. #2
    mfb
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    Re: E(1/sn) and var(1/sn)

    If you can find a distribution function for sn, you can transform it into a distribution function for 1/sn (there is a nice formula for that, but I do not know its name). Using this, you can calculate Var(1/sn).
    If the original probability distribution function is P_f(x) and you want to find the distribution of g(x), it is something like P_g(y)=\frac{P_f(g^{-1}(y))}{dg/dx} (check this), assuming g is invertible and differentiable.
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  3. #3
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    Re: E(1/sn) and var(1/sn)

    Thanks MFB
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