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2.33 X and Y are independent zero mean Gaussian random variables with variances sigma^2 x, and...

2.33 X and Y are independent zero mean Gaussian random variables with variances sigma^2 x, and sigma^2 y. Let Z = 1/2(X + Y) and W =1/2 (X - Y) a. Find the joint pdf fz, w(z, w). b. Find the marginal pdf f(z). c. Are Z and W independent?

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