# 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} }

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 NOTE ON CONFIDENCE REGIONS BASED ON THE BIVARIATE CHEBYSHEV INEQUALITY. APPLICATIONS TO ORDER STATISTICS AND DATA SETS.

- Mathematics
- 2014

#### References

SHOWING 1-5 OF 5 REFERENCES

A New Generalization of Chebyshev Inequality for Random Vectors

- Mathematics, Computer Science
- ArXiv
- 2007