Random variables X1 and X2 have zero expected value. The random vector X = [X1 X2] has a covariance matrix of the form

(a) For what values of α and β is C a valid covariance matrix?
(b) For what values of α and β can X be a Gaussian random vector?
(c) Suppose now that α and β satisfy the conditions in part (b) and X is a Gaussian random vector. What is the PDF of X2? What is the PDF of W = 2X1 - X2?

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