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AN ASYMPTOTIC EXPANSION FOR THE INSPECTION PARADOX

Published online by Cambridge University Press:  12 December 2005

J. E. Angus
J. E. Angus
Affiliation:
School of Mathematical Sciences, Claremont Graduate University, Claremont, CA 91711, E-mail: john.angus@cgu.edu
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Abstract

Suppose that there are n families with children attending a certain school and that the number of children in these families are independent and identically distributed random variables, each with probability mass function P{X = j} = pj, j ≥ 1, with finite mean μ = [sum ]j≥1jpj. If a child is selected at random from the school and XI is the number of children in the family to which the child belongs, it is known that limn→∞P{XI = j} = jpj /μ,j ≥ 1. Here, asymptotic expansions for P{XI = j} are developed under the condition E|X|3 < ∞.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 20 , Issue 1 , January 2006 , pp. 87 - 94
Copyright
© 2006 Cambridge University Press

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References

REFERENCES

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