Variance, Covariance

Variance

$= \sqrt{\mathrm{std}}$

$ \sigma_{x}^{2} = \frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})^2 $

 

Covariance

$ \sigma(x, y) = \frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x}) (y_i - \bar{y}) $

 

Covariance Matrix 

Example of a 2d covariance matrix:

$ C = \begin{bmatrix} \sigma(x,x) & \sigma(x,y) \\ \sigma(y,x) & \sigma(y,y) \\ \end{bmatrix} $

 

Diagonal Covariance Matrix 

Example of a 2d diagonal covariance matrix:

$ C = \begin{bmatrix} \sigma(x,x) & 0 \\ 0 & \sigma(y,y) \\ \end{bmatrix} $

 

 

Reference

datascienceplus.com/understanding-the-covariance-matrix/