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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. $X_i$ be the length of the $i$th piece. For example, in $01000110$, we have $X_1=1$, $X_2=3$, $X_3=0$, $X_4=1$. My question is whether r.v.s $X_i$ 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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migrated from cstheory.stackexchange.com Aug 3 '11 at 6:04

This question came from our site for theoretical computer scientists and researchers in related fields.

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
this is also out of scope for cstheory (see the faq). Try: stats.stackexchange.com –  Artem Kaznatcheev Jul 16 '11 at 18:05

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