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 |
| Publicado: |
Taylor & Francis Ltd
Aug2023
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| Materias: | |
| Acceso en línea: | Ver este registro en EBSCOhost |
| Sumario: | 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. |
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