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Vol. 13 No. 03 (2026)
Volume 13 Issue 03

Articles

COMPLETING PRACTICAL PROBLEMS INVOLVING A SEQUENCE OF INDEPENDENT TESTS, BERNOULLI SCHEMES, AND LIMIT THEOREMS

Published 2026-03-16

  • Davronov Doniyorbek Zarruxovich, Xakimova Mamura Muxammadievna

Davronov Doniyorbek Zarruxovich, Xakimova Mamura Muxammadievna
Student, Faculty of Service Samarkand Institute of Economics and Service, Assistant Lecturer Department of Higher Mathematics Samarkand Institute of Economics and Service

Abstract

In this article, we consider practical problems related to a sequence of independent trials, the Bernoulli scheme, and limit theorems in probability theory. Particular attention is paid to the application of these mathematical models in solving probability problems and analyzing random processes. In this paper, we explore the fundamental theoretical principles of the Bernoulli scheme, the conditions for independent trials, and their role in the formation of the binomial distribution. Limit theorems, which allow us to describe the behavior of probability variables over a large number of trials, are also considered. Examples of practical problems are provided demonstrating the use of these methods in educational processes and applied research.

Keywords

probability theory, independent trials, bernoulli scheme, binomial distribution, event probability, limit theorems, law of large numbers, central limit theorem, random variables, mathematical statistics.

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