Suppose : [0, ) [, ] be a function such that the function : [, ] [, ] defined by (x) := (ex) for all x [, ) is strictly increasing and convex on its domain. Moreover, assume that (R) R. Then show that FDPD,(g, f ) = Z R f 1 1 1 Z R f g 1 Z R g1 where f, g L, := {h : R R : h is measurable, R R h d = 1, R R h d < }, is a valid statistical distancealso known as the divergencefor each fixed > 0; i.e. you need to show that: (a) FDPD,(g, f ) 0 for all f, g L,. (Hint: Use Holder's inequality.) (b) FDPD,(g, f ) = 0 if and only if f = g