Measure of central tendency

variance is a natural measure of central tendancy, but there are others.

$q^{th}$ central moment: $\mathbb{E}[(X-\mathbb{E}X)^q]$

$q=2$ gives the variance

In proof of Hoeffding Inequality:

Idea in brief: Apply Markov’s Inequality to $\mathbb{E}[(X − \mathbb{E}X)^q]$ for larger q, or more generally to $f(X − \mathbb{E}X)$ for some other non-negative function $f$. E.g., to $\exp(X − EX)$.

References:

1. CS6763 Lecture 3, page 14