Probability distribution model for the number of balls called until someone "hits" a conventional bingo

Authors

  • Pedro Ferreira de Lima Universidade Federal Rural de Pernambuco/Universidade Regional do Cariri
  • Cláudio Tadeu Cristino Universidade Federal Rural de Pernambuco https://orcid.org/0000-0001-6748-209X
  • Paulo Renato Alves Firmino Professor da Universidade Federal do Cariri e Colaborador do Programa de Pós-Graduação em Biometria e Estatística Aplicada da Universidade Federal Rural de Pernambuco https://orcid.org/0000-0002-3308-2650
  • Cícero Carlos Felix Oliveira Doutorando pelo Programa de Pós-Graduação em Biometria e Estatística Aplicada - UFRPE, professor de estatística do IFCE - Campus Crato

Keywords:

bingo games, probability models, simulation, balls called

Abstract

This paper aims to obtain a model of the probability distribution for the random variable that counts the number of balls called until someone hit conventional bingo games. Starting from a basic model developed for a bingo with exactly one card, the distribution of the minimum of n independent random variables was used to expand the proposed n = 200 model, n = 1000, n = 2000, n = 5000 and n = 10000 cards. From a routine in R, 200 plays bingo were simulated for different numbers of cards cited above. With the results, adherence Kolmogorov-Smirnov tests were performed to verify the quality of the developed model. All models tested were approved at the level α = 0.05. The work is finished by making a comparison between the main measures of central tendency: mean, median and mode, calculated when used empirical distri-
butions obtained from simulations and theoretical construction. It was also observed that the differences between the distributions, both the absolute differences, the relative differences are very small, reinforcing what had been previously.

Author Biographies

Pedro Ferreira de Lima, Universidade Federal Rural de Pernambuco/Universidade Regional do Cariri

Aluno do programa do Programa de Pós-Graduação em Biometria e Estatística Aplicada - UFRPE/Recife-PE,           professor adjunto pela URCA/Juazeiro do Norte-CE

Cláudio Tadeu Cristino, Universidade Federal Rural de Pernambuco

Professor do Programa de Pós-Graduação em Biometria e Estatística Aplicada-UFRPE

References

BUSSAB, W. O. e MORETTIN, P. A., Estatística Básica- 5ª ed., São Paulo: Saraiva, 2006.

CHUNG, K. L. - A course in probability theory third edition, Standford University, Academic Press, San Diego, USA, 2001

LANGSETH, H. & LINDQVIST, B., - Competing Risks for Repairable Systems: A data study, Journal of Planning and Inference, vol 136(5), 1687-1700, 2005

MAGALHÃES, M. N. Probabilidade e Variável Aleatória, 2ª ed., São Paulo: EDUSP, 2006.

R CORE TEAM. - R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. 2012. ISBN 3-900051-07-0, URL: http://www.R-project.org/.

Published

11-11-2015

How to Cite

de Lima, P. F., Cristino, C. T., Firmino, P. R. A., & Oliveira, C. C. F. (2015). Probability distribution model for the number of balls called until someone "hits" a conventional bingo. Sigmae, 4(2), 6–13. Retrieved from https://publicacoes.unifal-mg.edu.br/revistas/index.php/sigmae/article/view/227

Issue

Section

Applied Statistics