D**u
发帖数: 204 | 1 Lemma: if p1+p2+...+pm=1. ( 0<= P(i) <= 1), then
a1^p1*...*am^pm <= a1*p1+...+am*pm.
Proof of your problem:
(q1/p1)^p1*...*(qm/pm)^pm <=(using Lemma) q1/p1*p1+...+qm/pm*pm =1
Then take log at both sides. | z***e
发帖数: 5600 | 2
Use Jensen's inequality. log is concave function, hence
log (\sum Pi*Xi) >= \sum Pi*log(Xi)
In your case Xi=Pi/Qi .
-Z. |
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