Multidimensional Chebyshev's inequality

In probability theory, the multidimensional Chebyshev's inequality is a generalization of Chebyshev's inequality, which puts a bound on the probability of the event that a random variable differs from its expected value by more than a specified amount. Let X {\displaystyle X} be an N {\displaystyle N} -dimensional random vector with expected value μ = E ⁡ [ X ] {\displaystyle \mu =\operatorname {E} [X]} and covariance matrix V = E ⁡ [ ( X − μ ) ( X − μ ) T ] .

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Multidimensional Chebyshev's inequality

In probability theory, the multidimensional Chebyshev's inequality is a generalization of Chebyshev's inequality, which puts a bound on the probability of the event that a random variable differs from its expected value by more than a specified amount. Let X {\displaystyle X} be an N {\displaystyle N} -dimensional random vector with expected value μ = E ⁡ [ X ] {\displaystyle \mu =\operatorname {E} [X]} and covariance matrix V = E ⁡ [ ( X − μ ) ( X − μ ) T ] .

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Source: Wikipedia "Multidimensional Chebyshev's inequality" · CC BY-SA 4.0

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