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# Variance of two jointly distributed Gaussian random variables

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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?

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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

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This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

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