Thou shalt not say "at random" in vain: Bertrand's paradox exposed
History and Overview
2019-08-23 v3 Probability
Abstract
We review the well known Bertrand paradoxes, and we first maintain that they do not point to any probabilistic inconsistency, but rather to the risks incurred with a careless use of the locution "at random". We claim then that these paradoxes spring up also in the discussion of the celebrated Buffon's needle problem, and that they are essentially related to the definition of (geometrical) probabilities on "uncountably" infinite sets. A few empirical remarks are finally added to underline the difference between "passive" and "active" randomness, and the prospects of any experimental decision
Cite
@article{arxiv.1810.07805,
title = {Thou shalt not say "at random" in vain: Bertrand's paradox exposed},
author = {Nicola Cufaro Petroni},
journal= {arXiv preprint arXiv:1810.07805},
year = {2019}
}
Comments
17 pages, 4 figures. Added: Appendix A; References 7, 8, 10; Modified: Abstract; Section 4; a few sentences elsewhere