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Q.4A random vector (X, Y, Z) has joint density given by . f (x, y,z) = k exp [ 1/2 (2x2 2xy + y2 +
Q.4A random vector (X, Y, Z) has joint density given by
. f (x, y,z) = k exp [ 1/2 (2x2 2xy + y2 + z2 + 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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