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