The Poisson distribution
The Poisson distribution models the probability of a number of events within a given time interval, assuming that these events occur with a known average rate and successive events occur independently of the time that has passed since the previous event.
A concrete example of a process that can be modeled by a Poisson distribution would be if an individual received an average of, say, 23 emails per day. If we assume that the arrival times for the emails are independent of each other, then the total number of emails an individual receives each day can be modeled by a Poisson distribution.
Another example could be the number of trains that stop at a particular station each hour. The PMF for a Poisson distribution is ...
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