DIRICHLET-RELATED PROBABILITY PROBLEMS AND NEW TOOLS FOR SOLVING THEM

In this paper we primarily consider waiting time problems under three different sampling rules. SR1 is the usual sampling with replacement, SR2 is without replacement, and SR3 is also with replacement, but uses no repetitions. We develop a new methodology for solving a wide variety of waiting time problems under each of the three sampling rules. A connection between waiting time problems under SR2 and SR3 is established which enables one to simultaneously solve waiting time problems under both of these sampling rules. The methods are illustrated with a large number of examples.