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DERIVATION OF THE PROBABILITY DISTRIBUTION

FUNCTIONS FOR SUCCESSION QUOTA RANDOM VARIABLES

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DEMETRIOS L. ANTZOULAKOS^{ 1} AND
ANDREAS N. PHILIPPOU^{ 2}

^{1} *Department of Economics, University of Crete,
Perivolia-Rethimno 74100, Greece*

^{2} *Department of Mathematics, University of Patras, Patras
26110, Greece*
(Received August 22, 1994; revised September 26, 1995)

**Abstract.**
The probability distribution
functions (pdf's) of the sooner and later waiting time
random variables (rv's) for the succession quota
problem (*k* successes 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.

*Key words and phrases*:
Succession quota,
sooner and later problems,
Bernoulli trials, binary
sequence of order *k*, probability distribution
function, probability generating function, longest run.

**Source**
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