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A stochastic process is a collection of random variables usually indexed by a totally ordered set.
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Probability that no three events happen in a pre-defined window
Let $G_j$ be the event that $\operatorname{gap}(j,j+2)>W$. In terms of the interarrival times $X_i$ we can write this as the event that $X_{j+1}+X_{j+2}>W$. The independence of the interarrival times …