Probabilities for a generalized birthday problem

Joseph Naus

Research output: Contribution to journalArticlepeer-review

62 Scopus citations


Let (Equation presented)1’s and M- (Equation presented) 0’s be randomly arranged in a row. Saperstein [11] defines the random variable k*mto be the maximum number of 1’s within any m consecutive positions in the arrangement, and finds Pr (k*m< k) for k > (Equation presented). This article derives the distribution of k*m, for all (Equation presented) for M/m = L, L an integer. Simplified forms are given for M/m = L, k > (Equation presented).

Original languageEnglish (US)
Pages (from-to)810-815
Number of pages6
JournalJournal of the American Statistical Association
Issue number347
StatePublished - Sep 1974

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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