@article {
author = {Chiu, Samuel S. and Larson, Richard C.},
title = {Bertrand’s Paradox Revisited: More Lessons about that Ambiguous Word, Random},
journal = {Journal of Industrial and Systems Engineering},
volume = {3},
number = {1},
pages = {1-26},
year = {2009},
publisher = {Iranian Institute of Industrial Engineering},
issn = {1735-8272},
eissn = {},
doi = {},
abstract = {The Bertrand paradox question is: “Consider a unit-radius circle for which the length of a side of an inscribed equilateral triangle equals 3 . Determine the probability that the length of a ‘random’ chord of a unit-radius circle has length greater than 3 .” Bertrand derived three different ‘correct’ answers, the correctness depending on interpretation of the word, random. Here we employ geometric and probability arguments to extend Bertrand’s analysis in two ways: (1) for his three classic examples, we derive the probability distributions of the chord lengths; and (2) we also derive the distribution of chord lengths for five new plausible interpretations of randomness. This includes connecting (and extending) two random points within the circle to form a random chord, perhaps being a most natural interpretation of random.},
keywords = {Bertrand paradox,geometrical probability,Randomness,Mathematical Modeling},
url = {http://www.jise.ir/article_3997.html},
eprint = {http://www.jise.ir/article_3997_6a52197644296c9501c5be1f63955e8a.pdf}
}