Abstract
We study the length of T-contaminated runs of heads in the well-known coin tossing experiment. A T-contaminated run of heads is a sequence of consecutive heads interrupted by T tails. For T=1 and T=2 we find the asymptotic distribution for the first hitting time of the T contaminated run of heads having length m; furthermore, we obtain a limit theorem for the length of the longest T-contaminated head run. We find the rate of the approximation of our accompanying distribution for the length of the longest T-contaminated head run. For the proof we use a powerful lemma of Csáki et al. (1987).
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