how to calculate E(1/x) and E(1/X^2)when given E(X)=3
Last edited by rajr; December 9th 2009 at 12:41 AM.
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Am i right in saying e(1/x)=1/e(x)=1/3 thank you
No, that's false And without any further information, it's not possible to calculate E[1/X]
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
Originally Posted by rajr 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 where f is the pdf of X. So just substitute here : I didn't explicitly write f, the pdf of a Gamma distribution, because there exist 2 versions of it.
Originally Posted by rajr 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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