Jensen's inequality Lemma. Let f be a convex function, and let X be a random variable. Then, f(EXDSElf(X) Proof. f(E[X)=f∑k,P{X=k} k=-∞0 Definition of expectation c 2001 by Charles E Leiserson Introduction to Agorithms Day17L9.13© 2001 by Charles E. Leiserson Introduction to Algorithms Day 17 L9.13 Jensen’s inequality Lemma. Let f be a convex function, and let X be a random variable. Then, f(E[X]) ≤ E[f(X)].   = ∑ ⋅ = ∞k=−∞ f (E[X ]) f k Pr{X k} Proof. Definition of expectation