Problem (3): (10 points) Given that: 2I(X;Y) 4(X,Y)=1- H(X)+H(Y) Show that A (X,Y) is a pseudo-metric of independence of the two random variables X and Y, i.e., it satisfies: O SA(X, Y) S1, 4(X, Y) = 1 when X, Y are completely independent 4(X, X) = 0 and 4(X, Y) = A (Y, X)