My Math Forum expected value

 March 13th, 2012, 10:59 PM #1 Member   Joined: Aug 2011 Posts: 71 Thanks: 0 expected value Let $b_i, i=1,...,n$ be real numbers. To the set of such vectors $b$ we put into correspondence the group $\Pi_n$ of all permutations $\pi$ of the set $\{1,...,n\}$ as $\pi(\cdot)=1, \mbox{if} \pi(i)\leq n/2$ and $\pi(\cdot)=-1, \mbox{if} \pi(i)>n/2=$ . How to calculate the following expectation: $E\left|\sum_{i=1}^{n/2}b_{\pi(i)}-\sum_{i=n/2+1}^nb_{\pi(i)}\right|^2$? Thank you.

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