Re: variance of product of random variables

*To*: mathgroup at smc.vnet.net*Subject*: [mg70090] Re: variance of product of random variables*From*: "ben" <benjamin.friedrich at gmail.com>*Date*: Tue, 3 Oct 2006 06:16:32 -0400 (EDT)*References*: <efq5iv$2ap$1@smc.vnet.net>

Dear Frank, All depends on the correlation functions (the linear and the higher ones) of the two variables a and b. If a and b were completly uncorrelated (not even non-linear correlations among them), then you can compute the variance of their product quite easily v(ab) := < a^2b^2 > - < ab >^2 = <a^2><b^2> - <a>^2<b>^2 = v(a) <b> + v(b) <a> + v(a) v(b); v(a)=<a^2>-<a>^2, v(b)=<b^2>-<b>^2 here v(.) denotes variance, <.> denotes mean. Note that we do not have to assume normal distributions for a and b, essential is that their are uncorrelated, hence the means of products factor into products of means. Bye Ben Frank Brand schrieb: > Dear Mathematica friends, > > is there a hint to a work done with Mathematica calculating the variance of a > product of two random variables that are normally distributed? > > Thanks in advance > Frank