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A LIMIT THEOREM FOR BERNOULLI RV'S AND FELLER'S SHOE PROBLEM
Author(s) -
Dwass M.
Publication year - 1985
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.1985.tb01154.x
Subject(s) - bernoulli's principle , mathematics , limit (mathematics) , poisson distribution , sequence (biology) , combinatorics , central limit theorem , bernoulli distribution , sample (material) , set (abstract data type) , distribution (mathematics) , discrete mathematics , random variable , mathematical analysis , statistics , computer science , physics , genetics , biology , thermodynamics , programming language
Consider n sets of objects, each set consisting of m distinct types (for instance n place settings each made up of m distinct dishes and silverware pieces.) s items are drawn at random from the mn items. The distribution of the number of complete sets (each consisting of all m items) in the sample of s is asymptotically Poisson distributed with parameter (a /m ) m if s = an 1–1 and n →∞. This fact can be interpreted in terms of a certain limit theorem for a sequence of i.i.d Bernoulli rv's.