Random chord in a circle and Bertrand's paradox: New generation method, extreme behaviour and length moments
Bull. Korean Math. Soc. 2021 Vol. 58, No. 2, 433-444
https://doi.org/10.4134/BKMS.b200345
Published online March 8, 2021
Printed March 31, 2021
Zoran Vidovi\'c
University of Belgrade
Abstract : In this paper a new generating procedure of a random chord is presented. This problem has its roots in the Bertrand's paradox. { A study of the limit behaviour of its maximum length and the rate of convergence is conducted.} In addition, moments of record values of random chord length are obtained for this case, as well as other cases of solutions of Bertrand's paradox.
Keywords : Bertrand's paradox, new solution, records, rate of convergence
MSC numbers : Primary 60D05, 60G70
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