Re: variance of product of random variables
- To: mathgroup at smc.vnet.net
- Subject: [mg70121] Re: variance of product of random variables
- From: "astanoff" <astanoff at gmail.com>
- Date: Wed, 4 Oct 2006 05:59:36 -0400 (EDT)
- References: <efq5iv$2ap$1@smc.vnet.net><eftdll$6c8$1@smc.vnet.net>
ben wrote: > 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. [...] Hi, Seems to me about variance of uncorrelated product, that instead of : v(a*b) = v(a)*<b> + v(b)*<a> + v(a)*v(b) (which is not homogeneous) it should rather be : v(a*b) = v(a)*<b>^2 + v(b)*<a>^2 + v(a)*v(b) V.Astanoff