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?
>