\(X\)为随机变量, \(p(x)\)为它的概率密度或质量函数.
期望
\[\mu = E(X) = \int_{-\infty}^{{+\infty}} x p(x) dx
\]
方差
\[\sigma^2 = D(X) = \int_{-\infty}^{{+\infty}} (x - \mu)^2 p(x)dx \\= \int_{-\infty}^{{+\infty}} x^2 p(x) dx + \int_{-\infty}^{{+\infty}} \mu^2 p(x) dx - 2\mu \int_{-\infty}^{{+\infty}} x p(x) = E(X^2) - E^2(X)
\]
\(\sigma\)为标准差.