2. Assume the numbers 12, 2 and are specified, with i2 > 0 and [1,1]. Suppose you want to generate random variables X1 and X2 that have variances 12 and 2, as well as correlation . You can do it by starting with independent standard normal variables Z1 and Z2 (assuming you have access to random outcomes from a normal distribution).

(i) For constants a, b, and c, let X1 = aZ1 and X2 = bZ1 + cZ2. Compute Cov(X1, X2) and (X1, X2). (ii). How should a, b, and c be determined so that Xi has variance i2 and the correlation between X1 and X2 is ?