Abstract
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 (Formula presented.). 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.
Original language | English (US) |
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Pages (from-to) | 301-303 |
Number of pages | 3 |
Journal | American Statistician |
Volume | 77 |
Issue number | 3 |
DOIs |
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State | Published - 2023 |
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- General Mathematics
- Statistics, Probability and Uncertainty
Keywords
- Dynamic-programming
- Prime number theorem
- Stopping time