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February 16th, 2011, 09:27 PM   #1
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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.
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February 16th, 2011, 09:53 PM   #2
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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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