What is 'Jensen's Inequality'?

What is 'Jensen's Inequality'?

Approach: Relate the expectation of a function to the function of an expectation.

For a convex function f, E[f(X)] ≥ f(E[X]). For a concave function, the inequality is reversed. It is fundamental in risk analysis and information theory.

Follow-up: Is f(x) = x^2 convex or concave?

Key concepts: convexity, concavity, expected value.