Summary
A limit theorem is proved for the waiting time till each of a given set of lengthn patterns occurs as a run in a sequence of i.i.d. random variables distributed uniformly on {1,2,...,d}. A heuristic approach called the independence principle is introduced which can be applied to similar problems connected with waiting times.
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Móri, T.F. On the waiting time till each of some given patterns occurs as a run. Probab. Th. Rel. Fields 87, 313–323 (1991). https://doi.org/10.1007/BF01312212
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DOI: https://doi.org/10.1007/BF01312212