Explicit multivariate bounds of Chebyshev type

Abstract. In the paper, Chebyshev type upper bounds are presented for the probability that a random vector \(X\) falls outside of an ellipsoid, in terms of the mean and variance of \(X\). Our inequalities are better than those found in the literature.

Key words and phrases. Chebyshev inequality, Selberg inequality, diagonally symmetric distribution.