A LIMIT THEOREM FOR BERNOULLI RV'S AND FELLER'S SHOE PROBLEM

M. Dwass

Statistica Neerlandica, 1985, vol. 39, issue 4, 357-360

Abstract: 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 = an1–1 and n→∞. This fact can be interpreted in terms of a certain limit theorem for a sequence of i.i.d Bernoulli rv's.

Date: 1985
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