# Jensen inequality

Let $LaTeX: f$ be convex on $LaTeX: X$, and let $LaTeX: x$ be a random variable with expected value, $LaTeX: E(x)$. Then, $LaTeX: E(f(x)) \ge f(E(x))$. For example, let $LaTeX: X=R$ and $LaTeX: f(x) = x^2$. Suppose $LaTeX: x$ is normally distributed with mean zero and standard deviation $LaTeX: s$. Then,
$LaTeX: E(f(x)) = E(x^2) = s^2 \ge 0 = E(x) = f(E(x))$.