Question

X and Y are discrete jointly distributed discrete valued random variables. The relation between their joint entropy H(X,Y) and their individual entropies H(X),H(Y) is

H(X,Y)≤H(X)+H(Y), equality holds when X,Y are independent

H(X,Y)≤H(X)+H(Y), equality holds when X,Y are uncorrelated

H(X,Y)≥H(X)+H(Y), equality holds when X,Y are independent

H(X,Y)≥H(X)+H(Y), equality holds when X,Y are uncorrelated