A very simple proof of the multivariate Chebyshev's inequality

@article{Navarro2016AVS,
  title={A very simple proof of the multivariate Chebyshev's inequality},
  author={J. Navarro},
  journal={Communications in Statistics - Theory and Methods},
  year={2016},
  volume={45},
  pages={3458 - 3463}
}
  • J. Navarro
  • Published 2016
  • Mathematics
  • Communications in Statistics - Theory and Methods
Abstract In this short note, a very simple proof of the Chebyshev's inequality for random vectors is given. This inequality provides a lower bound for the percentage of the population of an arbitrary random vector X with finite mean μ = E(X) and a positive definite covariance matrix V = Cov(X) whose Mahalanobis distance with respect to V to the mean μ is less than a fixed value. The main advantage of the proof is that it is a simple exercise for a first year probability course. An alternative… Expand
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A simple proof for the multivariate Chebyshev inequality
A New Generalization of Chebyshev Inequality for Random Vectors
Chebyshev's inequality for Banach-space-valued random elements