Negative Dependence Through the FKG Inequality

We investigate random variables arising in occupancy problems, and show the variables to be negatively associated, that is, negatively dependent in a strong sense. Our proofs are based on the FKG correlation inequality, and they suggest a useful, general technique for proving negative dependence among random variables. We also show that in the special case of two binary random variables, the notions of negative correlation and negative association coincide. ∗This work was supported by the ESPRIT II Basic Research Actions Program of the EC under contract no. 7141 (project ALCOM II) and by the Danish National Research Foundation through the Centre for Basic Research in Computer Science (BRICS). †Work partly done when the authors were visiting Max-Planck-Institut für Informatik, Saarbrücken. Desh Ranjan also acknowledges the hospitality of BRICS.