X. DECORRELATING RANDOM VARIABLES If X and Y have a covariance of cov[X, Y], we can transform them to a new pair of random variables whose covariance is zero. To do so we let W = X Z = aX +Y a) Express cov[X, X + Y] in terms of var [X] and cov[X, Y]. b) Using your result from part a), find the value of a such that cov[W, Z] = 0. This process is called decorrelating the random variables