Three zero mean, unit variance random variables X,Y, and Z 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 1/2, and Y and Z have a correlation coefficient of -1/2.
(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.