> [!NOTE] Theorem > Let $(\Omega,\mathcal{F},\mathbb{P})$ be a [[Probability Space|probability space]]. Let $X:\Omega\to \mathbb{R}^{+}_{0}$ be a non-negative [[Continuous random variables|cts real-valued random variable]] variable on $(\Omega,\mathcal{F},\mathbb{P}).$ Then its [[Expectation of Integrable Continuous Real-Valued Random Variable|expectation]] satisfies $\mathbb{E}[X] = \int_{0}^{\infty} \mathbb{P}(X>x) \, dx $