Exercise 4. (More Properties of Joint PDF/PMF) (25pt). (a) Show that for every y such that fy(y) > 0 we have that fxy(xly)dx = 1. Explain every step of the proof. (b) (Independence v.s. Correlation) We know from class that independent random vari- ables are uncorrelated. However, the opposite is not true in general and uncorrelated random variables can be dependent. Consider a pair of random variables (X, Y) with the pmf given by PxY(x, y) 0 Owl- OWI- O Show that X and Y are uncorrelated, but not independent. (Justify every step of you computation.)