most recent 30 from http://mathoverflow.net 2013-05-24T12:33:45Z http://mathoverflow.net/feeds/question/92494 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/92494/expected-value-of-partial-sum-of-iids-given-the-full-sum id0 2012-03-28T19:39:10Z 2012-03-28T20:22:35Z

<p>Hi </p> <p>I need to calculate $ES_n|S_m$ for $S_i=\sum_i X_i$ and $X_i$ are some iid (not a specific distribution), and $m>n$ . ie, calculate the expected value of a partial sum given the entire sum. I think it's just the partial sum, $\frac{n}{m}\cdot S_m$ but I don't know how to prove it. Trying to explicitly use the expectation definition didn't go anywhere.</p> <p>Thanks</p> <p>[edit] The best I could do is symmetry - because if I look at one $EX_i|S_n$ it should be equal for each i, then they should be the same. But it's not really a proof...</p>