triangle inequality with random variables

by axk   Last Updated January 15, 2018 21:19 PM

Suppose $a$ and $b$ are real numbers (positive in my case), $X$ is a random variables and $F$ is a set of function. Are the following true?

  1. $|a-b| \le E_X|a-X|+E_X|X-b|$

  2. $|a-b| \le E_X [\inf_{f\in F} (|a-f(X)| + |f(X)-b|)] $



Related Questions


Log probability vs product of probabilities

Updated June 23, 2017 18:19 PM

How many failed both classes

Updated November 04, 2017 17:19 PM


Random Walk Probability Including Drift

Updated April 28, 2017 14:19 PM