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Let $a_i$ be $n$ distinct real numbers. What is the expectation:

$\mathbb E_\sigma \left[ \sum_{i=1}^{n} \frac {1} {a_{\sigma(i)} - \sum_{j=1}^{i-1}a_{\sigma(j)}} \right] $

where the expectation is taken over all $n!$ permutations $\sigma:[1,2,..,n]\rightarrow[1,2,..,n]$

I appreciate your help.

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    can you please explain me more?$i$didn't understand the development. also i dont understand how it get along with my previous comment2012-12-20

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