Chebyshev's Inequality is a statistical theorem that provides a way to estimate the proportion of values that lie within a certain number of standard deviations from the mean in any distribution. This inequality states that for any real-valued random variable with a finite mean and variance, at least $1 - \frac{1}{k^2}$ of the observations will fall within $k$ standard deviations from the mean, where $k > 1$. This concept is crucial in random projections and dimensionality reduction techniques, as it helps in understanding how data behaves when projected into lower-dimensional spaces.
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