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In a poisson process, we have both lambda occurences per unit time (on average) and 1/lambda waiting time for the first occurence (and for each subsequent occurence)

Is this universal? Is it the case that any process that has discrete occurences in time, with average number of occurences in a second a, has an expected time between occurences 1/a

(I presume we'd need some sort of uniformity hypothesis, to prevent a process that always has a fixed interval between odd and even ocurrences, and other processes like that)

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