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If $\log(X)\sim N(a,b^2)$ for a random variable $X$, what is the expectation of $\frac{1}{X}$?

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$E[X^s] = e^{s a + \frac{1}{2} s^2 b^2 }$. See Wikipedia. –  Calvin Lin May 27 '13 at 19:07
    
Wow... I appreciate moments significantly more now. Thanks! –  Derek May 27 '13 at 19:16

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up vote 1 down vote accepted

If $\log(X) \sim N(a,b^2)$ then $\log(1/X)=-\log(X)\sim N(-a,b^2)$, so the question is: if $\log Y\sim N(-a,b^2)$ then what is $\mathbb E(Y)$? (Can you take it from there?)

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Nice use of symmetry! –  Derek May 27 '13 at 21:42

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