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Post Closed as "off topic" by Bill Johnson, Andreas Blass, Gerald Edgar, Brendan McKay, Douglas Zare
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Hi 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. Thanks [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... |
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expected value of partial sum of iids given the full sumHi 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. Thanks
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