Question: A random vector (X, Y, Z) has joint density given by . f (x, y,z) = k exp [ 1/2 (2x 2 2xy + y

A random vector (X, Y, Z) has joint density given by . f (x, y,z) = k exp [ 1/2 (2x 2 2xy + y 2 + z 2 + 2x 6y) . 1. Compute k. 2. Compute the expectations P(X), P(Y ) and P(Z). 3. Compute the density of the random vector (X, Z). 4. Compute the correlation coeffificient between X and Z and between X and Y . 5. Let W = X + Z; compute the probability density of W

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