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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 be an N-dimensional random vector with expected value μ = E {\displaystyle \mu =\operatorname {E} } and covariance matrix
If V {\displaystyle V} is a positive-definite matrix, for any real number t > 0 {\displaystyle t>0} :
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