(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, , with the expected value of
. It states that
where .
I find Markov’s inequality to be beautiful for 2 reasons:
- It applies to both continuous and discrete random variables.
- 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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