On some probability distributions, related to the classical Bernoulli scheme

Authors

  • Sergey M. Ananjevskii St Petersburg State University, 7–9, Universitetskaya nab., St Petersburg, 199034, Russian Federation
  • Valery B. Nevzorov St Petersburg State University, 7–9, Universitetskaya nab., St Petersburg, 199034, Russian Federation

DOI:

https://doi.org/10.21638/spbu01.2022.202

Abstract

For more than three centuries, the classical scheme of independent Bernoulli trials, starting with the work of Jacob Bernoulli, has been one of the most popular topics in probability theory. It is ideal for setting and solving various practical problems. Many results have been obtained related to modifications of this scheme, but new situations and new problems appear that require further progress in the study of various random variables associated to one degree or another with independent Bernoulli trials. Solutions to some of these problems are presented in this paper.

Keywords:

Bernoulli scheme, binomial distribution, geometric distribution, generating functions

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References

Литература

1. Феллер В. Введение в теорию вероятностей и ее приложения, пер. с англ. Т. 1. Москва, Мир (1984).

2. Balakrishnan N., Nevzorov V.B. A primer on statistical distributions. Hoboken, New Jersey,John Wiley & Sons (2003).

3. Иванов О.А. Схема Бернулли и обобщения чисел Фибоначчи. Вестник Санкт-Петербургского университета. Математика. Механика. Астрономия 1 (59), вып. 4, 529–532 (2014).

References

1. Feller W. An introduction o probability theory and its applications. Vol.1. New York, JohnWiley & Sons (1968). [Rus. ed.: Feller W. Vvedenie v teoriju verojatnostej i ee prilozhenija. Moscow, Mir Publ. (1984)].

2. Balakrishnan N., Nevzorov V.B. A primer on statistical distributions. Hoboken, New Jersey, John Wiley & Sons (2003).

3. Ivanov O.A. Bernoulli scheme and generalizations of Fibonacci numbers. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 1 (59), iss. 4, 529–532 (2014). (In Russian)

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Published

2022-07-06

How to Cite

Ananjevskii, S. M., & Nevzorov, V. B. (2022). On some probability distributions, related to the classical Bernoulli scheme. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 9(2), 201–208. https://doi.org/10.21638/spbu01.2022.202

Issue

Vol. 9 No. 2 (2022)

Section

Mathematics

License

Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.