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Math Help - how to calculate E(1/x)

  1. #1
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    Question how to calculate E(1/x)

    how to calculate E(1/x) and E(1/X^2)when given E(X)=3
    Last edited by rajr; December 9th 2009 at 01:41 AM.
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  2. #2
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    Am i right in saying e(1/x)=1/e(x)=1/3 thank you
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  3. #3
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    No, that's false

    And without any further information, it's not possible to calculate E[1/X]
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  4. #4
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    Sorry I should have explained the question in detail

    X~Gamma(a,3)

    i.e. am i right in saying the inverse of the distribution is 1/X~Gamma(a,1/3).

    Therefore E(1/X)=1/3a and Var(1/X)=1/3(a^2)

    Thanks for your response
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  5. #5
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    Quote Originally Posted by rajr View Post
    Sorry I should have explained the question in detail

    X~Gamma(a,3)

    i.e. am i right in saying the inverse of the distribution is 1/X~Gamma(a,1/3).
    No you are not...

    For any bounded function g, we have E[g(X)]=\int_{\mathbb{R}} f(x)g(x) ~dx
    where f is the pdf of X.

    So just substitute here :
    E[1/X]=\int_{\mathbb{R}} \tfrac 1x \cdot f(x) ~dx

    I didn't explicitly write f, the pdf of a Gamma distribution, because there exist 2 versions of it.
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  6. #6
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    Quote Originally Posted by rajr View Post
    Sorry I should have explained the question in detail

    X~Gamma(a,3)

    i.e. am i right in saying the inverse of the distribution is 1/X~Gamma(a,1/3).

    Therefore E(1/X)=1/3a and Var(1/X)=1/3(a^2)

    Thanks for your response
    Does it agree with what is here: Inverse-gamma distribution - Wikipedia, the free encyclopedia
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