# Variance of two jointly distributed Gaussian random variables

Not what you're looking for? Search our solutions OR ask your own Custom question.

Let X and Y be two jointly distributed Gaussian random variables with means ηX and ηY and variance σ2X and σ2Y respectively. The correlation coefficient between X and Y is ρ. Let Z be a new random variable defined by Z = X-Y. Is Z Gaussian? What is the variance of Z?

© BrainMass Inc. brainmass.com October 7, 2022, 6:43 pm ad1c9bdddfhttps://brainmass.com/statistics/variance/variance-two-jointly-distributed-gaussian-random-variables-314420

## SOLUTION This solution is **FREE** courtesy of BrainMass!

Let X and Y be two jointly distributed Gaussian random variables with means ηX and ηY and variance σ2X and σ2Y respectively. The correlation coefficient between X and Y is ρ. Let Z be a new random variable defined by Z = X-Y. Is Z Gaussian? What is the variance of Z?

Solution. In general, Z is not Gaussian. But, when ρ=0, Z is Gaussian. To find the variance of Z, we do the following

See Attached

© BrainMass Inc. brainmass.com October 7, 2022, 6:43 pm ad1c9bdddf>https://brainmass.com/statistics/variance/variance-two-jointly-distributed-gaussian-random-variables-314420