043. The Poisson Distribution

Developed by the French mathematician Simeon Poisson (1781 - 1840), the Poisson distributions Is a discrete probability distribution that measures the probability of a random event over some interval of time and space. The Poisson distribution is also useful as an approximation for binomial probabilities.

It is often used to describe the number of arrivals of customers per hour, the number of industrial accidents each month, or the number of machines that break down and are awaiting repair. In each of these cases, the random variable (customers, accidents, machines) is measured per unit of time and space (distance).

For application of the Poisson distribution two Assumptions are necessary:

1. The probability of the occurrence of the event is constant for any two intervals of time or space.

2. The occurrence of the event in any interval is independent of the occurrence in any other interval.

The Poisson probability function can be expressed as

, (4.15)

Where X is number of times the event occurs; μ is the mean of occurrence per unit of time or space; E = 2.71828 is the base of natural logarithm system.

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