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expected value of inner products of iid standard normal vactorsvectors

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Hello,

I wish to calculate (or upper bound) expectations of the form E[^2], $E[\langle x,y \rangle^2]$, where x $x$ and y $y$ are i.i.d standard gaussian vectors of length n. Are there any exponential type upper bounds for the same?

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expected value of inner products of iid standard normal vactors

Hello,

I wish to calculate (or upper bound) expectations of the form E[^2], where x and y are i.i.d standard gaussian vectors of length n. Are there any exponential type upper bounds for the same?