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Derivation of the probability distribution functions for succession quota random variables. (English) Zbl 0925.62036

Summary: The probability distribution functions (pdf’s) of the sooner and later waiting time random variables (rv’s) for the succession quota problem (\(k\) sucesses and \(r\) failures) are derived presently in the case of a binary sequence of order \(k\). The probability generating functions (pgf’s) of the above rv’s are then obtained directly from their pdf’s. In the case of independent Bernoulli trials, expressions for the pdf’s in terms of binomial coefficients are also established.

MSC:

62C05 General considerations in statistical decision theory
60E10 Characteristic functions; other transforms
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