$\begin{vmatrix}~E\Big[\sum \limits_{i=1}^{n}X_i\Big]~\end{vmatrix} \le \sum \limits_{i=1}^{n}\begin{vmatrix}E[X_i]\end{vmatrix}$

30 Views Asked by At

What's the name of this inequality:

$$\begin{vmatrix}\sum \limits_{i=1}^{n}X_i\end{vmatrix} \le \sum \limits_{i=1}^{n}\begin{vmatrix}X_i\end{vmatrix}$$

$$\begin{vmatrix}~E\Big[\sum \limits_{i=1}^{n}X_i\Big]~\end{vmatrix} \le \sum \limits_{i=1}^{n}\begin{vmatrix}E[X_i]\end{vmatrix}$$