Abstract

{n probability theory, one of the classical trends in probability theory is research related to the so-called Bernoulli sequences of random variables (r.v.).    We are talking about independent random variables X1, X2,… taking value 1 with some probability p, 0<p<1, and value 0 with probability q=1-p. Often in such publications the event {Xn=1} is interpreted as "success in the-th test", and its complement – the event {Xn=0} – as "failure in this test". In this paper we will give a short review of the results obtained earlier in this area and some new results.

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