The exponential distribution is continuous and the Poisson distribution is discrete, yet the two distributions are closely related.

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The Poisson distribution models the number of events that occur within a fixed interval of time or space, while the exponential distribution models the time between events in a Poisson process. Therefore, the two distributions are closely related, even though one is discrete and one is continuous. In fact, if the number of events in a fixed time interval follows a Poisson distribution with mean λ, then the time between events follows an exponential distribution with rate λ.

The Exponential Distribution Is Continuous and the Poisson Distribution Is