On an interval splitting problem

F. Thomas Bruss*, S. Rao Jammalamadaka, Xian Zhou

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


Let X1, X2,..., be i.i.d. random variables, which are uniformly distributed on [0,1]. Further let I1(0) = [0, 1] and let Ik(n) denote the kth largest interval generated by the points 0, X1, X2,..., Xn-1, 1 (or equivalently, the interval corresponding to the kth largest spacing at the nth stage). This note studies the question for which classes of sequences k = k(n), will the interval Ik(n)(n) be hit (a.s.) only finitely often, as well as infinitely often.

Original languageEnglish
Pages (from-to)321-324
Number of pages4
JournalStatistics and Probability Letters
Issue number4
Publication statusPublished - 1990
Externally publishedYes


  • extended Borel-Cantelli lemma
  • Interval splitting
  • spacing


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