An Extreme Value Theory for Long Head Runs *

  title={An Extreme Value Theory for Long Head Runs *},
  author={Louis I. Gordon and Mark F. Schilling and Michael S. Waterman},
For an infinite sequence of independent coin tosses with P(Heads)=pE(O, l), the longest run of consecutive heads in the first n tosses is a natural object of study. We show that the probabilistic behavior of the length of the longest pure head run is closely approximated by that of the greatest integer function of the maximum of n(1 p ) i.i.d. exponential random variables. These results are extended to the case of the longest head run interrupted by k tails. The mean length of this run is shown… CONTINUE READING
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