AISM 52, 407-414

## Sooner and later waiting time problems

based on a dependent sequence

### Qing Han and Sigeo Aki

Department of Informatics and Mathematical Science, Graduate
School of Engineering Science, Osaka University, Osaka 560-8531, Japan

(Received July 30, 1998; revised February 15, 1999)

Abstract.
This paper introduces a new concept: a binary sequence of order (*k, r*), which
is an extension of a binary sequence of order *k* and a Markov dependent sequence. The probability functions of the sooner and later waiting time random variables are derived in the binary sequence of order (*k, r*). The probability generating functions of the sooner and later waiting time distributions are also obtained. Extensions of these results to binary sequence of order (*g, h*) are also presented.

Key words and phrases:
Binary sequence of order (*k, r*), binary sequence of order *k*,
sooner and later waiting time problems, probability function, probability generating function.

**Source**
( TeX , DVI )