Chebyshev's Inequality is a statistical theorem that provides a way to estimate the probability that a random variable deviates from its mean. Specifically, it states that for any real-valued random variable with a finite mean and variance, the proportion of observations that lie within k standard deviations from the mean is at least $$1 - \frac{1}{k^2}$$ for any k > 1. This inequality is fundamental in probabilistic methods as it allows combinatorialists to make probabilistic statements about distributions without requiring specific assumptions about their shape.
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