均值 (Mean):
\[\overline{x}=\frac{1}{n}\sum_{i=1}^{n} x_i \]方差 (Variance): 衡量单类样本偏离均值的程度
\[D(x)=\frac{1}{n}\sum_{i=1}^{n}(x_i-\overline{x})^2 \]协方差 (Covariance): 反映两个随机变量的相关程度
\[\begin{aligned} \text{Cov}(x,y) &= E(X-EX)(Y-EY) \\ &= \frac{1}{n}\sum_{i=1}^{n} (x_i-\overline{x})(y_i-\overline{y}) \\ &= E(XY) - EX\cdot EY \\ &= \frac{1}{n}\sum_{i=1}^{n} x_i y_i -\overline{x}\cdot\overline{y} \end{aligned} \]相关性 (Correlation): 标准化协方差
\[\begin{aligned} \rho(x,y) &= \frac{\text{Cov}(x,y)}{\sqrt{D(x)}\sqrt{D(y)}} \\ &= \frac{\sum_{i=1}^{n} (x_i-\overline{x})(y_i-\overline{y})}{\sqrt{\sum_{i=1}^{n}(x_i-\overline{x})^2}\sqrt{\sum_{i=1}^{n}(y_i-\overline{y})^2}} \end{aligned}\]皮尔森相关性 (Pearson Correlation): 数据中心化后两个n维向量的夹角余弦
标签：frac,sum,sqrt,overline,协方差,一些,aligned,统计 From： https://www.cnblogs.com/4thirteen2one/p/16609247.html