
Re: Variance for a linear combination of three (normal) random variables
Posted:
Jun 28, 2006 8:23 AM


"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.

