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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.

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Isn’t it straightforward? I think that it is easy to show that if i≠j and t≤t′, then Pr[Xi≥s | Xj=t] ≥ Pr[Xi≥s | Xj=t′], and that this implies that any two random variables in X1,…,X(n+1) are negatively correlated. – Tsuyoshi Ito Jul 15 '11 at 18:18
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this is also out of scope for cstheory (see the faq). Try: stats.stackexchange.com – Artem Kaznatcheev Jul 16 '11 at 18:05

migrated from cstheory.stackexchange.com Aug 3 '11 at 6:04

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