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2014 | 34 | 1-2 | 23-34
Tytuł artykułu

An extended problem to Bertrand's paradox

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EN
Abstrakty
EN
Bertrand's paradox is a longstanding problem within the classical interpretation of probability theory. The solutions 1/2, 1/3, and 1/4 were proposed using three different approaches to model the problem. In this article, an extended problem, of which Bertrand's paradox is a special case, is proposed and solved. For the special case, it is shown that the corresponding solution is 1/3. Moreover, the reasons of inconsistency are discussed and a proper modeling approach is determined by careful examination of the probability space.
Twórcy
  • School of Engineering Technology, State University of New York, Farmingdale, NY, USA
  • Department of Statistics, University of Wyoming Laramie, WY, USA
Bibliografia
  • [1] L. Basano and P. Ottonello, The ambiguity of random choices: probability paradoxes in some physical processes, Amer. J. Phys. 64 (1996) 34-39. doi: 10.1119/1.18289.
  • [2] J.L.F. Bertrand, Calcul des Probabilities (Gauthier-Villars, Paris, 1889).
  • [3] S.S. Chiu and R.C. Larson, Bertrand's paradox revisited: more lessons about that ambiguous word, random, Journal of Industrial and Systems Engineering 3 (2009) 1-26.
  • [4] M. Gardiner, Mathematical games: problems involving questions of probability and ambiguity, Scientific American 201 (1959) 174-182.
  • [5] J. Holbrook and S.S. Kim, Bertrand's paradox revisited, Mathematical Intelligencer 22 (2000) 16-19.
  • [6] E.T. Jaynes, Probability Theory: The Logic of Science (Cambridge University Press, New York, 2003).
  • [7] E.T. Jaynes, Well-posed problem, Foundations of Physics 3 (1973) 477-493.
  • [8] L. Marinoff, A resolution of Bertrand's paradox, Philosophy of Science 61 (1994) 1-24. doi: 10.1086/289777.
  • [9] G.J. Szekely, Paradoxes in Probability Theory and Mathematical Statistics (Kluwer Academic Publishers, New York, 1986).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1160
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