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Topic: Variance for a linear combination of three (normal) random variables
Replies: 3   Last Post: Jun 28, 2006 9:51 AM

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Michael Jørgensen

Posts: 148
Registered: 12/13/04
Re: Variance for a linear combination of three (normal) random variables
Posted: Jun 28, 2006 8:23 AM
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"Konrad Viltersten" <tmp1@viltersten.com> wrote in message
news:4gfa2vF1locgaU1@individual.net...
> Suppose there's a sum as follows:
> X := a * W_1 + b * W_2 + c * W_3
>
> How can we compute the variance of X? Well, it's rather
> uncomplicated if one can be assured of independency.
> Now, if one is assured that they _ARE_ dependent (as
> for instance, being three states of a Wiener process at
> three consecutive times), is there anything else to do but
> sit down and cry loudly like a confused child?
>
> Of, course, it's obvious that X ~ N(0,s^2) and that every
> W_i ~ N(0,i). But how can we use it?!


Well, if the W_i are not independent, then you need to know there
correlation/covariance.

Specifically, you need to calculate E{X^2}, and that involves terms like
E{W_1*W_2}, etc.

-Michael.





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