On the Probability That Two Random Integers Are Coprime

• Lei, Jing ^[1] ; Kadane, Joseph B. ^[1]
  1. [1] Carnegie Mellon University

     Carnegie Mellon University

     City of Pittsburgh, Estados Unidos

     
• Localización: Statistical science, ISSN 0883-4237, Vol. 35, Nº. 2, 2020, págs. 272-279
• Idioma: inglés
• DOI: 10.1214/19-STS737
• Texto completo no disponible (Saber más ...)
• Resumen

  • We show that there is a nonempty class of finitely additive probabilities on N2 such that for each member of the class, each set with limiting relative frequency p has probability p. Hence, in that context the probability that two random integers are coprime is 6/π2. We also show that two other interpretations of “random integer,” namely residue classes and shift invariance, support any number in [0,6/π2] for that probability. Finally, we specify a countably additive probability space that also supports 6/π2.