Question

Redo the proof of Jensen's inequality, but using notation from probability theory. You will need to convert certain expressions into conditional expectations and then use the law of total expectation in your proof by induction. The statement you prove should be something like the following: 3.1. Let f : R → R be a convex function. Then for any n E Z²², any finite probability space with n-element outcome space N, and any X : N –→ R, we have that E(f(X)) > f(E(X)). Your focus should be translating the notation of the proof from class; you can refer to the posted notes for the course if you need to verify the steps made in the original proof.

Appreciate! This should be done from probability theory.

Answer 1

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