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I am lost with the signs cancellation. Please help me to calculate this inner pruduct.

Let $a$ and $b$ be two $2m$ dimentional vectors such that their entries are Rademacher random variables and such that the sum of the variables for each vector is zero. i.e. $$P(a_i=1)=P(a_i=-1)=P(b_i=1)=P(b_i=-1)=\frac{1}{2}$$ and $$ \sum\limits_{i=0}^{2m}a_i=\sum\limits_{i=0}^{2m}b_i=0 $$ Find the inner product $\langle a,b\rangle$.

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    As far as I understand you need to find expcted value of the inner product. Right?2012-07-18
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    Yes, my real question is a p-th moment of the inner product. Thats why I am started from the consudering the inner product itself.2012-07-18
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    Are this random vector independent?2012-07-18
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    The vectors a and b are independetnt. Dependence only between the coordinates of the vector a and between the coordinates of the vector b.2012-07-18
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    So you should mention all this in your question2012-07-18
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    But I've mentioned conditions on the entries of the vectors and right now my question is find an inner product...2012-07-18

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