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A BALANCE SCALE PROBLEM

Published online by Cambridge University Press:  28 March 2013

Mark Brown
Mark Brown*
Affiliation:
Department of Mathematics, The City College, CUNY, NY E-mail: mbrown@ccny.cuny.edu
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Abstract

Suppose we have n objects of different weights. We randomly sample pairs of objects, and for each sampled pair use a balance scale to determine which of the two objects is heavier. It is assumed that the sequence of sampled pairs is iid, each selection uniformly distributed on the set of n(n−1)/2 pairs. We continue sampling until the first time that we can definitively identify the heaviest of the n objects. The problem of interest is to compute the expected number of selected pairs.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 27 , Issue 2 , April 2013 , pp. 141 - 146
Copyright
Copyright © Cambridge University Press 2013

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References

1.Barlow, R.E. & Proschan, F. (1975). Statistical theory of reliability and life testing: probability models. New York: Holt, Rinehart and Winston, Inc.Google Scholar
2.Brown, M. (1975). The first passage time distribution for a parallel exponential system with repair. In Reliability and fault tree Analysis, Barlow, R.E., et al. (eds) Philadelphia, PA: SIAM. pp. 365–396.Google Scholar
3.Ross, S.M. (2007). Introduction to probability models, 9th ed.Amsterdam: Elsevier.Google Scholar
4.Ross, S.M. & Pekoz, E. (2007). A second course in probability. Boston, MA: http://www.ProbabilityBookstore.com.Google Scholar