> [!NOTE] Definition 1 (Square-Integrable Continuous Real-Valued Random Variable) > Let $X$ be a [[Continuous random variables|continuous real-valued random variable]] whose [[Probability Density Function|probability density function]] is given by $f_{X}.$ Then $X$ is square-integrable iff the integral $\int_{-\infty}^{\infty} x^{2} f_{X}(x) \, dx $[[Absolutely Convergent Series|converges absolutely]]: that is, $X^{2}$ is [[Integrable Real-Valued Random Variable|integrable]]. # Properties The [[Variance of a Square-Integrable Continuous Real-Valued Random Variable|variance]] of $X$ is given $\text{Var}(X)=\mathbb{E}[(X-\mathbb{E}[X])^{2}].$