Abstract
Let F0 be the event that l0 0-runs of length k0 occur and F1 be the event that l1 1-runs of length k1 occur in a two-state Markov chain. In this paper using a combinatorial method and the Markov chain imbedding method, we obtained explicit formulas of the probability generating functions of the sooner and later waiting time between F0 and F1 by the non-overlapping, overlapping and "greater than or equal" enumeration scheme. These formulas are convenient for evaluating the distributions of the sooner and later waiting time problems.
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