Mathematical Statistics Lesson of the Day – Markov’s Inequality

(This article was originally published at The Chemical Statistician » Statistics, and syndicated at StatsBlogs.)

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 have useful implications for understanding a data set.


Filed under: Mathematical Statistics, Mathematics, Probability, Statistics, Statistics Lesson of the Day Tagged: continuous random variable, discrete random variable, expected value, finite expected value, Markov's inequality, probability, random variable



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