The Poisson distribution is a mathematical rule that assigns probabilities to the number of occurrences of a certain event. It is most commonly used to model the number of random occurrences of some phenomenon in a specified unit of space or time. The Poisson distribution is one of the most important in probability. It is usually written as: P(x) = (^xe^-)/x!, where P(x) is the probability that the outcome of the function will be x, and is the average number of occurrences in a specified interval, either of space or time. In a Poisson distribution the mean and variance are equal and can be described by: E(x) = Var(x) = .

There are four assumptions made in order to apply the Poisson distribution to a problem. First, it is assumed that the probability of observing a single event over a small interval, either...