article · 1998

Surprise Maximization

J.M. Borwein, J. M. Borwein, P. Marechal

Cited by 0Abstract and details only

Abstract

The optimization problems arising from an information theoretic formulation of the Surprise Examination (or Unexpected Hanging) Paradox are examined and solved. They provide a nice application of both the Kuhn-Tucker Theorem and the Jensen inequality. Keywords Surprise examination paradox, entropy optimization, Kuhn-Tucker conditions, Jensen inequality. 1 1 Introduction In this paper, we study the optimization problems arising from an entropic approach to the so-called Surprise Examination (or Unexpected Hanging) Paradox. The idea of such an approach was proposed by Karl Narveson and presented in a recent article by Timothy Y. Chow [1]. (We shall not discuss here the different approaches to the resolution of the paradox itself; the reader interested in these aspects is invited to consult [1].) An event (such as a test given by a teacher or a surprise tax audit) occurs once every m days, with probability p i on day i, i = 1; : : : ; m. We wish to find a probability distribution t...

Cite this paper

APA 7

Borwein, J., Borwein, J. M., & Marechal, P. (1998). Surprise Maximization.

MLA 9

Borwein, J.M., et al. “Surprise Maximization.” 1998.

Chicago

Borwein, J.M., J. M. Borwein, and P. Marechal. 1998. “Surprise Maximization.”

Harvard

Borwein, J., Borwein, J.M. and Marechal, P. (1998) ‘Surprise Maximization’.

BibTeX

@article{borwein1998surprise,
  title = {{Surprise Maximization}},
  author = {Borwein, J.M. and Borwein, J. M. and Marechal, P.},
  year = {1998}
}

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