Variance (Continuous Version)

variance (continuous case)

The variance of a continuous rv $X$ with PDF $f (x)$ and mean value $μ$ is:

σ^{2} = σ_{X}^{2} = Var (X) = \int_{- \infty}^{\infty} (x - μ)^{2} \cdot f (x) d x = E [(X - μ)^{2}]

The standard deviation of $X$ is $σ = σ_{X} = SD (X) = \sqrt{Var (X)}$ .