Three random variables X, Y, and Z have zero means and variances of 2, 3, and 4respectively. The three random variables are added to form a new random variable, W

=X+Y + Z. Random variables X and Y are uncorrelated, X and Z have a correlation coefficient of 1/3, and Y and Z have a correlation coefficient of – 1/3. (a) Find the variance of W. (b) Find the correlation coefficient between W and X. (c) Find the correlation coefficient between W and the sum of Y and Z.