We have a string consisting n "1"s and m "0"s. Consider a random permutation of the string. The "1"s divide all "0"s into n+1 consecutive pieces (including those of length 0). Let r.v. Xi be the length of the ith piece. For example, in 01000110, we have X1=1, X2=3, X3=0, X4=1. My question is whether r.v.s Xi are negatively associated/regressive? I couldn't find any ref on this but I think this might have been looked at before. Thanks a lot.