I cannot prove the following inequality, which I state below:
Let p,q be two positive real numbers such that p+q=1. Let f and g be two probability density functions. Then, show that:
∫Rp2f2+q2g2pf+qg≥p2+q2 .
I tried to use Cauchy-Schwarz and even Titu's lemma, but got nowhere. Any help will be greatly appreciated. Thanks!
No comments:
Post a Comment