Question: 3. Suppose that you have a function f : R -> R that satisfies the Jensen inequality E(f (X)) f(E(X)) for every probability measure and

3. Suppose that you have a function f : R -> R that satisfies the Jensen inequality E(f (X)) f(E(X)) for every probability measure and for every random variable X. Prove that the function f is convex. Hint: at some point in your proof you will need to define a probability space and random variable if you are going to use the assumption about f

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