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MathGroup Archive 2006

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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


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