(Kullback Leibler divergence between discrete random variables:) Let X and Y be two discrete random variables with non-zero pmf defined on the set of integers {1,2,...,m}. (a) Show that the function g(x) = ln x x + 1 0. (Hint: Show that g"(x) < 0 and find its unique maxima to establish the inequality.) (b) Using In x < x-1 from part (a), show that, m px(i) In Px (i) i=1 0, py (i) (13) with equality occuring only if px (i) = py(i) for all i = 1,2,..., m. (Hint: Work with the negative of expression on the LHS of the inequality.)