4. Suppose that f and g are two P.M.F.'s defined over 1, 2,3, ..., such that f(x) > 0 and g(x) > 0 for each r = 1, 2,3, .... Define D(f, g) = E (- log six) for X ~ f (this turns out to be a useful quantity for comparing distributions, and is important in information theory and in statistical physics). (a) Which is larger, D(f, g) or - log E (b) What is the value of - log E