If an object selected randomly from a universe has property $\Pi$ with positive probability, then there exists an object in the universe that has property $\Pi.$ > [!NOTE] Theorem > For a probability space over $\Omega$ (the sample space) and random variable $X : \Omega → R$ such that $E[X] = μ$, $\mathbb{P}[X ≥ μ] > 0$ and $\mathbb{P}[X ≤ μ] > 0$. Equivalently, there exists $x, y \in \Omega$ such that $X(x)\geq \mu$ and $X(y)\leq \mu.$