A Simple Proof for the Multivariate Chebyshev Inequality¶
Navarro, J. (1305/2013). A Simple Proof for the Multivariate Chebyshev Inequality.
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Domain-specific¶
- Chebyshev's Inequality
- If \(\sigma>0\), setting \(t=k\sigma\) gives the familiar \(1/k^2\) bound; when \(\sigma=0\), the unnormalized inequality still holds trivially but division by \(\sigma\) is undefined.
This sourceNavarro supplies the scalar Markov derivation and a new proof of the finite-vector inequality attributed there to Chen's earlier result; the displayed inverse-covariance formula requires positive-definite \(V\).
- If \(\sigma>0\), setting \(t=k\sigma\) gives the familiar \(1/k^2\) bound; when \(\sigma=0\), the unnormalized inequality still holds trivially but division by \(\sigma\) is undefined.
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