Infinite entropy. This problem shows that the entropy of a discrete random variable can be infinite. Let A = (n logn). [It is easy to show that A is finite by bounding the infinite sum by the integral of (x log x)-.] Show that the integer-valued random vari- able X defined by Pr(X = n) = (An log n)-1 for n = 2, 3, ..., has H(X) = +0.