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4. Random variables X and Y have joint density function fx,y (r, y) = 5x21512-6xy 10 (a) What is the joint density function of Z

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4. Random variables X and Y have joint density function fx,y (r, y) = 5x21512-6xy 10 (a) What is the joint density function of Z = X + Y and W = X - Y? [15 mins] (b) Are W and Z independent? 5 mins] (c) What is Cov(X, Y)? Hint: consider Var(Z) - Var(W).] [10 mins]

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