Abstract

The classical scheme of independent Bernoulli trials has been one of the most popular topics in probability theory for more than three centuries (starting with the works of Jacob Bernoulli). This scheme is ideal for formulating and solving various practical problems. Many results have been obtained using modifications of this scheme; however, new situations and new problems appear, and they require further advancement in the study of various random variables somehow related to independent Bernoulli trials. In this work, we continue to study some problems related to a series of successes and failures in sequences of Bernoulli random variables. This paper represents a direct continuation of our work “On Some Probability Distributions Related to the Classical Bernoulli Scheme” published in 2022.

中文翻译：

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关于与经典伯努利方案相关的一些概率分布。二

摘要

三个多世纪以来，独立伯努利试验的经典方案一直是概率论中最受欢迎的主题之一（从雅各布伯努利的作品开始）。该方案非常适合制定和解决各种实际问题。使用该方案的修改已经获得了许多结果；然而，新情况、新问题不断出现，需要进一步研究与独立伯努利试验相关的各种随机变量。在这项工作中，我们继续研究与伯努利随机变量序列中的一系列成功和失败相关的一些问题。这篇论文代表了我们 2022 年发表的“关于与经典伯努利方案相关的一些概率分布”的工作的直接延续。