On Groups And Series Of Successes And Failures In Bernoulli Schemes

Abstract

One of the most popular areas of interest in the probability theory is the research related to Bernoulli random variables. In Bernoulli sequence of independent and identically distributed random variables \(X_1\), \(X_2\), \(...\) taking the values \(1\) (one) with some probability \(p\), \(0 \lt p \lt 1\) and \(0\) (zero) with probability \(q =1-p\). It will be interesting to find the probability of successes before any number of failures. In this paper we will consider groups and series of successes and failures in Bernoulli sequence.