Prove Theorem 7.2.20.
a. Show that, using (7.2.19), we can write

and, since (r+1) is a maximum,

When is the inequality and equality?
b. Now use Jensen's inequality to show that

Which together with part (a) proves the theorem.

Transcribed Image Text:

E [logk(Xlar-+ i ) , y)@r), У] E [log k(XIjr)' y)0 r),y].