(Solution Library) Compute the mean and variance of W=12+8X-6Y+Z, and the correlation coefficient of X and Y, where for random variables X, Y, and Z: E(X)=2, E(Y)=3,
Question: Compute the mean and variance of \(W=12+8X-6Y+Z\), and the correlation coefficient of X and Y, where for random variables X, Y, and Z:
- \(E\left( X \right)=2\), \(E\left( Y \right)=3\), \(E\left( Z \right)=-5\)
- var (X) = 4, var (Y) = 12, var(Z) = 15
- cov(X, Y) = -2, cov(X, Z) = 3, cov (Y, Z) = 7
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