Hitting a Prime in 2.43 Dice Rolls (On Average)

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dc.contributor.authorAlon, Noga
dc.contributor.authorMalinovsky, Yaakov
dc.date.accessioned2022-10-14T15:40:10Z
dc.date.available2022-10-14T15:40:10Z
dc.date.issued2023-05-15
dc.description.abstractWhat is the number of rolls of fair 6-sided dice until the first time the total sum of all rolls is a prime? We compute the expectation and the variance of this random variable up to an additive error of less than 10−4 , showing that the expectation is 2.4284.. and the variance is 6.2427... This is a solution of a puzzle suggested a few years ago by DasGupta in the Bulletin of the IMS, where the published solution is incomplete. The proof is simple, combining a basic dynamic programming algorithm with a quick Matlab computation and basic facts about the distribution of primes.en_US
dc.description.urihttps://www.tandfonline.com/doi/full/10.1080/00031305.2023.2179664en_US
dc.format.extent5 pagesen_US
dc.genrejournal articlesen_US
dc.genrepresentations (communicative events)
dc.genrepreprintsen_US
dc.identifierdoi:10.13016/m2hupy-pnvs
dc.identifier.citationAlon, Noga, and Yaakov Malinovsky. “Hitting a Prime in 2.43 Dice Rolls (On Average).” The American Statistician 77, no. 3 (July 3, 2023): 301–3. https://doi.org/10.1080/00031305.2023.2179664.
dc.identifier.urihttps://doi.org/10.1080/00031305.2023.2179664
dc.identifier.urihttp://hdl.handle.net/11603/26187
dc.language.isoen_USen_US
dc.publisherTaylor & Francis
dc.relation.isAvailableAtThe University of Maryland, Baltimore County (UMBC)
dc.relation.ispartofUMBC Mathematics Department Collection
dc.relation.ispartofUMBC Faculty Collection
dc.rightsThis is the submitted manuscript of an article published by Taylor & Francis in The American Statistician on 15 May 2023, available online: http://www.tandfonline.com/doi/10.1080/00031305.2023.2179664en_US
dc.titleHitting a Prime in 2.43 Dice Rolls (On Average)en_US
dc.typeTexten_US
dcterms.creatorhttps://orcid.org/0000-0003-2888-674Xen_US

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