# Mathematical Statistics Lesson of the Day – Markov’s Inequality

Markov’s inequality is an elegant and very useful inequality that relates the probability of an event concerning a non-negative random variable, $X$, with the expected value of $X$.  It states that

$P(X \geq c) \leq E(X) \div c,$

where $c > 0$.

I find Markov’s inequality to be beautiful for 2 reasons:

1. It applies to both continuous and discrete random variables.
2. It applies to any non-negative random variable from any distribution with a finite expected value.

In a later lesson, I will discuss the motivation and intuition behind Markov’s inequality, which has useful implications for understanding a data set.