Chebyshev's inequality

Let be a random variable having finite mean and finite variance . Let be a strictly positive constant. Then, the following inequality, called Chebyshev's inequality, holds:

Thus, Chebyshev's inequality gives an upper bound to the probability that the absolute deviation of from its mean exceeds a certain threshold .

More details about Chebyshev's inequality can be found in the lecture entitled Basic probabilistic inequalities.

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