Analysis
It will be assumed that the events are occurring randomly with an average frequency of f. That is, they constitute a Poisson process. The probability that an event will occur in an infinitesimal time interval dt is then f dt. It follows that the probability P(t) that an event will occur at time t to t+dt with no events occurring between t=0 and time t is given by the exponential distribution (Lucke 1974, Meeks 2008):
The expected time between events is then
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