2. (3 points) Exercise 7.4 of [Oppenheim & Verghese].

The random variables X and Y have

E[X] = -1, E[Y] =2, E[X²] =9, E[XY] = −4, E[Y²] = 7.

(a) Let Z = 2X - Y + 5, and W = X + Y-1. Calculate the covariance zw of Z and W.

(b) If X and Y are bivariate Gaussian, what is the joint density of Z and W? (Hint: Utilize the fact

that affine combinations of bivariate Gaussian random variables are bivariate Gaussian.)