Poisson Distribution Poisson distribution is a type of probability distribution that is useful in describing the number of events that will occur in a specific period of time or in a specific area or volume. Typical examples of random variables where the Poisson probability distribution can be used are: The number of industrial accidents per month at a manufacturing plant. The parts per million of some toxin found in the water or air emission from a manufacturing plant. The number of customer arrivals per unit of time at a supermarket checkout counter.

Characteristics of a Poisson Random Variable:

Characteristics of a Poisson Random Variable 1. The problem consists of counting the number of times a certain event occurs during a given unit of time or in a given area or volume. 2. The probability that the event occurs in a given unit of time, area, or volume is the same for all units. 3. The number of events that occur in one unit of time, area, or volume is independent of the number that occur in any other mutually exclusive unit. 4. The mean or expected number of events in each unit is denoted by the Greek letter lambda, λ.

Probability Distribution, Mean, and Variance for a Poisson Random Variable:

Probability Distribution, Mean, and Variance for a Poisson Random Variable

Probability Distribution, Mean, and Variance for a Poisson Random Variable Cont.:

Probability Distribution, Mean, and Variance for a Poisson Random Variable Cont.

Poisson Probability Distribution:

Poisson Probability Distribution Suppose a musical equipment store can expect two customers every four minutes, on average. What is the probability that three or fewer customers will arrive at the musical equipment store in a 12 minute period ? We can expect 6 customers in a 12 minute period, therefore 6 = λ.

Poisson Probability Distribution cont.:

Poisson Probability Distribution cont.

Poisson Probability Distribution cont.:

Poisson Probability Distribution cont.

References:

References McClave, James T., Benson, P. George, Sincich, Terry. (2008). Statistics: For Business and Economics. New Jersey: Pearson Prentice Hall . http://www.youtube.com/watch?v=LlV6q4y1Uts&feature=fvwrel

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