  We investigate Mahonian and Eulerian probability distributions given by
inversions and descents in general finite Coxeter groups. We provide uniform
formulas for the means and variances in terms of Coxeter group data in both
cases. We also provide uniform formulas for the double-Eulerian probability
distribution of the sum of descents and inverse descents. We finally establish
necessary and sufficient conditions for general sequences of Coxeter groups of
increasing rank under which Mahonian and Eulerian probability distributions
satisfy central and local limit theorems.
