Question: Suppose X and Y are zero mean jointly normal random variables with equal variances, and correlation coefficient doesn't equal to zero. 1) Is there a

Suppose X and Y are zero mean jointly normal random variables with equal variances, and correlation coefficient doesn't equal to zero.

1) Is there a value for the coefficient a for which the random vairables (aX+Y) and (X-Y) are independent?

2) Find the variance of Z=X2+Y2, where alpha and beta are constants.

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