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tneurure
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Posts: 1
Joined: October 4th, 2005, 3:36 pm

Covariance

March 10th, 2010, 1:16 am

This might be a stupid question but...Assuming I generate two random normal numbers (r1 and r2) with variances v1 and v2.Set x1 and x2 to be:x1 = (r1 * a) + (r2 * b)x2 = (r1 * c) + (r2 * d)Now, figuring out the variances of x1 and x2 is no problem, but is there a formula for cov(x1,x2)?Thanks in advance.
 
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alexrem
Posts: 12
Joined: April 3rd, 2009, 4:57 pm

Covariance

March 10th, 2010, 1:34 am

By linearity of covariance you would have cov(x1, x2)=ac cov(r1, r1)+ bd cov (r2, r2) + (ad+bc)cov(r1, r2) = ac (v1)+ bd (v2) + (ad+bc)cov(r1, r2).You need to know the covariance between r1 and r2, knowing only their variances is not enough to do the question. By the way, you also need to know the covariance of r1 and r2 to figure out the variance of x1 and x2, for examplevariance of x1 is a^2(v1)+b^2(v2)+2ab cov(r1, r2)
Last edited by alexrem on March 9th, 2010, 11:00 pm, edited 1 time in total.
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