=+t−1 k=j Wk for j > 1. The number of such success runs starting in the first n positions is given by S = 

α∈I Xα, where the index set I = {1,...,n}.

The Poisson heuristic suggests the S is approximately Poisson with mean λ = pt

[(n−1)(1−p)+ 1]. Let Nα = {β ∈ I : |β −α| ≤ t}. Show that Xα is independent of those Xβ with β outside Nα. In the ChenStein bound (14.3), prove that 

α∈I