On Some Probability Distributions Related to the Classical Bernoulli Scheme. II

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.