Chebyshev's Inequality states that for a random variable with finite variance, the probability that it deviates from its mean by more than k standard deviations is at most one divided by k squared. Named for Pafnuty Chebyshev, it applies to any distribution with finite variance regardless of shape, and it underlies the standard proof of the weak law of large numbers.
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StatementChebyshev's inequality states that for a random variable with finite nonzero variance, the probability the variable deviates from its mean by more than k standard deviations is at most 1 divided by k squared, for any positive real number k. 1 Classification
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Source Chebyshev's Inequality (Wikipedia)
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1. Chebyshev's Inequality (Wikipedia)
Wikimedia Foundationlead section, first paragraph
Chebyshev's inequality (also called the Bienaymé-Chebyshev inequality) provides an upper bound on the probability of deviation of a random variable (with finite variance) from its mean.
History section
The theorem was first proved by Bienaymé in 1853 and more generally proved by Chebyshev in 1867.
Proved By: Pafnuty Chebyshev, Lead
The theorem is named after Russian mathematician Pafnuty Chebyshev, although it was first formulated by his friend and colleague Irénée-Jules Bienaymé. The theorem was first proved by Bienaymé in 1853 and more generally proved by Chebyshev in 1867.
In Group: Probability Theory, Lead section
In probability theory, Chebyshev's inequality (also called the Bienaymé-Chebyshev
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