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Relationship between Exponential and Poisson Distribution
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The Poisson distribution was concerned with counting the number of arrivals
that take place in some interval of time (where the term "arrival" refers
to some event that we count).
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The exponential distribution is concerned with looking at the time between
successive arrivals.
Both use the same parameter l which represents
a rate.
More specifically, suppose X is a Poisson r.v. with parameter
l , so that the expected number of arrivals
per unit time is equal to l. Then the random
variable T representing the time between successive arrivals follows an
exponential distribution with parameter l.
Jayant Rajgopal
