Maximizing the expected range from dependent observations under   mean-variance information
  In this article we derive the best possible upper bound for $E[\max{X_i}-\min_i{X_i}]$ under given means and variances on $n$ random variables $X_i$. The random vector $(X_1,...,X_n)$ is allowed to have any dependence structure, provided $E X_i=\mu_i$ and $Var X_i=\sigma_i^2$, $0<\sigma_i<\infty$. We provide an explicit characterization of the $n$-variate distributions that attain the equality (extremal random vectors), and the tight bound is compared to other existing results.   Key words and phrases: Range; Dependent Observations; Tight Expectation Bounds; Extremal Random Vectors; Probability Matrices; Characterizations. 
Nickos Papadatos
stat.ME