Consider a sequence of events and suppose the interarrival times between successive events are exponential with a common parameter λ. Denote by Mn the maximum among the first n interarrival times. As n approaches infinity, the distribution of the normalized random variable Mn/log(n) (i.e. P(Mn/log(n) < x)) converges to e^-x.
Added by David Y.
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Step 1
First, we need to find the distribution of Mn. Since the interarrival times are exponential with parameter &, the probability density function of the interarrival time is f(x) = &e^(-&x), for x > 0. Show more…
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