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A Generalized Birthday Problem

Frank H. Mathis
SIAM Review
Vol. 33, No. 2 (Jun., 1991), pp. 265-270
Stable URL: http://www.jstor.org/stable/2031144
Page Count: 6
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A Generalized Birthday Problem
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Abstract

A generalized version of the birthday problem is as follows. Suppose each member of a population independently receives a number randomly selected from {1, 2, 3, ⋯, x}, and a random sample of size n is to be taken. If $0 < p < 1$, what is the smallest value of n so that the probability that at least two of the sample have the same number is at least p? Both empirical modeling and approximation techniques are used to determine n as a function of x when p is fixed. An error analysis of the approximation is presented.

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