Let X and Y be jointly distributed Gaussian random variables, where the joint (X, Y) is distributed as a bivariate Gaussian distribution given by $egin{bmatrix} X \ Y end{bmatrix} sim Nleft(egin{bmatrix} 1 \ -1 end{bmatrix}, egin{bmatrix} 1 & -2 \ -2 & 9 end{bmatrix} ight)$ Define a random variable Z := 2X - 2Y (which may or may not be normally distributed). What is the variance of Z?
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So, the variance of 2X is 4 times the variance of X, and the variance of 2Y is 4 times the variance of Y. Second, we know that the variance of the sum (or difference) of two random variables is the sum of their variances minus (or plus) twice their covariance, if Show more…
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