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Chebyshev's inequality
Bound on probability of a random variable being far from its mean
Chebyshev's inequality
In probability theory, 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. More specifically, the probability that a random variable deviates from its mean by more than k σ {\displaystyle k\sigma } is at most 1 / k 2 {\displaystyle 1/k^{2}} , where k {\displaystyle k} is any positive constant and σ {\displaystyle \sigma } is the standard deviation (the square root of the variance). The rule is often called Chebyshev's theorem, about the range of standard deviations around the mean, in statistics. The inequality has great utility because it can be applied to any probability distribution in...
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