Hitting a Prime in 2.43 Dice Rolls (On Average).
What is the number of rolls of fair six-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 . This is a solution to a puzzle suggested by DasGupta in the Bulletin of the...
| Publicado en: | American Statistician Vol. 77; no. 3; pp. 301 - 304 |
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| Autores principales: | , |
| Formato: | Artículo |
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Taylor & Francis Ltd
Aug2023
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| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=ssf&AN=169847633&site=ehost-live header: @attributes: shortDbName: ssf uiTerm: 169847633 longDbName: Social Sciences Full Text (H.W. Wilson) uiTag: AN controlInfo: bkinfo: jinfo: jid: 00031305 STT jtl: American Statistician issn: 00031305 maglogo: Y pubinfo: dt: Aug2023 vid: 77 iid: 3 pid: 377 pub: Taylor & Francis Ltd artinfo: ui: 169847633 10.1080/00031305.2023.2179664 ppf: 301 ppct: 3 formats: tig: atl: Hitting a Prime in 2.43 Dice Rolls (On Average). aug: au: Alon, Noga Malinovsky, Yaakov affil: Department of Mathematics, Princeton University, Princeton, NJ Schools of Mathematics and Computer Science, Tel Aviv University, Tel Aviv, Israel Department of Mathematics and Statistics, University of Maryland, Baltimore County, Baltimore, MD su: Prime number theorem Mathematical statistics Dynamic programming Random variables sug: subj: Prime number theorem Mathematical statistics Dynamic programming Random variables keyword: Dynamic-programming Stopping time Dynamic-programming Stopping time ab: What is the number of rolls of fair six-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 . This is a solution to a puzzle suggested by DasGupta in the Bulletin of the Institute of Mathematical Statistics, 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. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: N holdings: @attributes: islocal: N |
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