February 16th, 2011, 09:27 PM  #1 
Newbie Joined: Aug 2009 Posts: 7 Thanks: 0  Jensen's inequality for log x
Hi all, I am seriously mixed up with a question which me and my fren have difference, which is the correct function for jensen inequality for all X E(Log(X))>= Log (E(X)) or E(Log(X))<= Log (E(X)) I remember Log as strictly concave, so shouldnt it be the 2nd 1? Please advise, need help to clear my doubt. 
February 16th, 2011, 09:53 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Jensen in equality for log x
I had never heard of Jensen's inequality before, but after looking it up, my inclination is the first choice is true since (as you said) the log functions are concave, and Jensen's inequality generalizes the statement that a secant line of a convex function lies above the graph. So, choice 2 would apply to a convex function, not a concave function. http://en.wikipedia.org/wiki/Jensen%27s_inequality 

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