> [!NOTE] Definition 1 (Square-Integrable Continuous Real-Valued Random Variable) > Let $X$ be a [[Square-Integrable Continuous Real-Valued Random Variable|square-integrable continuous real-valued random variable]] whose [[Probability Density Function|probability density function]] is given by $f_{X}.$ The variance of $X$ is given by $\text{Var}(X)=\mathbb{E}[(X-\mathbb{E}[X])^{2}]$where $\mathbb{E}$ denotes [[Expectation of Continuous Uniform Distribution|expectation]]. # Properties By [[Alternative Formula for Variance of a Square-Integrable Continuous Real-Valued Random Variable]], $\text{Var}(X)=\mathbb{E}[X^{2}]-\mathbb{E}[X].$