most recent 30 from http://mathoverflow.net 2013-05-24T09:39:53Z http://mathoverflow.net/feeds/user/12338 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/52563/approximating-expectation unradis 2011-01-19T23:50:05Z 2011-01-20T01:30:53Z

<p>if we are given a finite number N of points drawn from a probability distribution, expectation can be approximated as a finite sum over these points: E[f]=(1/N)(summation of f(x) over these N points).</p> <p>comparing this to the actual calculation of E[f]=summation of p(x)f(x), won't the difference between the actual value and approximate value be a lot in cases where p(x) varies a lot?</p>