# Jensen's Inequality

If \(f\) is a convex function, and \(x\) is a random variable then:

\begin{equation} E\left[ f(x) \right] \ge f\left( E[x] \right) \end{equation}

If \(f\) is a convex function, and \(x\) is a random variable then:

\begin{equation} E\left[ f(x) \right] \ge f\left( E[x] \right) \end{equation}