> [!NOTE] Definition 1 (Expectation of Integrable Continuous Real-Valued Random Variable) > Let $X$ be an [[Integrable Continuous Real-Valued Random Variable|integrable continuous real-valued random variable]] whose [[Probability Density Function|probability density function]] is given by $f_{X}.$ Then the *expectation* $X$ is given by $\mathbb{E}[X]=\int_{-\infty}^{\infty} x f_{X}(x) \, dx. $ # Properties # Applications **Examples**: