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Bertrand `paradox' reloaded (with details on transformations of variables, an introduction to Monte Carlo simulation and an inferential variation of the problem)

2015/04/06 by Giulio D'Agostini, D'Agostini, Giulio
Mathematics · Physics and Astronomy · #Data Analysis #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #History and Overview (math.HO) #Other Statistics (stat.OT) #Statistics and Probability (physics.data-an) #math.HO #physics.data-an #stat.OT

paper · pdf · doi:10.48550/arxiv.1504.01361

55 pages, 31 figures. Note based on lectures to PhD students in Rome. Android app available at http://www.roma1.infn.it/~dagos/prob+stat.html#bpr

arxiv created 2015/04/06 · arxiv updated 2018/02/12

Abstract

This note is mainly to point out, if needed, that uncertainty about models and their parameters has little to do with a `paradox'. The proposed `solution' is to formulate practical questions instead of seeking refuge into abstract principles. (And, in order to be concrete, some details on how to calculate the probability density functions of the chord lengths are provided, together with some comments on simulations and an appendix on the inferential aspects of the problem.)

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