most recent 30 from http://mathoverflow.net 2013-05-22T00:09:37Z http://mathoverflow.net/feeds/question/81921 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/81921/expected-value-of-inner-products-of-iid-standard-normal-vectors TC 2011-11-25T21:18:53Z 2011-11-25T22:10:13Z

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

http://mathoverflow.net/questions/81921/expected-value-of-inner-products-of-iid-standard-normal-vectors/81925#81925 Igor Rivin 2011-11-25T21:58:03Z 2011-11-25T22:10:13Z

<p>I must be misunderstanding the question, but <code>$&lt;x, y&gt;^2$</code> is a sum of the terms of the form $x_i x_j y_i y_j.$ The expectation of this term vanishes, unless $i=j,$ in which case it (the . expectation) is the square of the expectation of the square of the standard Gaussian. The square of the standard gaussian is the chi-square distribution with one degree of freedom, whose mean is $1,$ so the whole thing should be $n$.</p>