This cannot be solved without some knowledge of the joint distribution of X and Z
and of Y and Z. (At least the covariance in these distributions.)
Jon Cryer
At 07:52 PM 3/7/2003 +0100, you wrote:
Hi everybody,
I currently try to solve a problem that ends up with the question "What is the product of two normal distributions?". Unfortunately, I found nothing useful so far.
Now here is my problem:
I have two normally distributed variables X and Y. These variables are not independent.
The covariance cov(X,Y) = E(XY) - E(X)*E(Y) is not zero.
What I would like to know is: How does the covariance change, if I add a normally distributed variable Z (with Mu_Z = 0, Sigma_Z != 0) to Y?
Can I calculate cov(X,Y+Z) based on cov(X,Y) and Sigma_Z ?
Since E(Y + Z) = E(Y), all I would need is some clou on how E(X*(Y+Z)) looks like. But unfortunately, I don't know so far how X*(Y+Z) looks like.
I am thankful for any help!
Stefan
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Jon Cryer, Professor Emeritus Dept. of Statistics www.stat.uiowa.edu/~jcryer and Actuarial Science office 319-335-0819 The University of Iowa home 319-351-4639 Iowa City, IA 52242 FAX 319-335-3017
"It ain't so much the things we don't know that get us into trouble.
It's the things we do know that just ain't so." --Artemus Ward
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