Markov's Inequality states that for a non-negative random variable, the probability that it exceeds a positive value a is at most the expected value of the random variable divided by a. Named for Andrey Markov, it is one of the most basic tail bounds in probability theory and is used in turn to derive Chebyshev's Inequality.
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StatementMarkov's inequality states that for a nonnegative random variable X and any positive constant a, the probability that X is at least a is at most the expected value of X divided by a. 1 Classification
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Source Markov's Inequality (Wikipedia)
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1. Markov's Inequality (Wikipedia)
Wikimedia Foundationlead section, first paragraph
In probability theory, Markov's inequality gives an upper bound on the probability that a non-negative random variable is greater than or equal to some positive constant.
In Group: Probability Theory, Lead section
In probability theory, Markov's inequality gives an upper bound on
Proved By: Pafnuty Chebyshev, Lead
It is named after the Russian mathematician Andrey Markov, although it appeared earlier in the work of Pafnuty Chebyshev (Markov's teacher), and many sources, especially in analysis, refer to it as Chebyshev's inequality (sometimes, calling it the first Chebyshev inequality, while referring to Chebyshev's inequality as the second Chebyshev inequality) or Bienaymé's inequality.
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