If X(1), X(2), ..., X(n) are independent random variables, not necessarily with the same distribution, what is the variance of Z = X(1) X(2) ... X(n)? It turns out that the computation is very simple: In particular, if all the expectations are zero, then the variance of the product is equal to the product of the variances. See here for details. A More Complex System Even more surprising, if and…
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