4.5. The Poisson Probability Distribution http://www.ck12.org
4.5 The Poisson Probability Distribution
Learning Objectives
- Know the definition of the Poisson distribution.
- Identify the characteristics of the Poisson distribution.
- Identify the type of statistical situation to which the Poisson distribution can be applied.
- Use the Poisson distribution to solve statistical problems.
The Poisson distribution is useful for describing the number of events that will occur during a specific interval of
time or in a specific distance, area, or volume. Examples of such random variables are:
- The number of traffic accidents at a particular intersection.
- The number of house fire claims per month that is received by an insurance company.
- The number of people who are infected with the AIDS virus in a certain neighborhood.
- The number of people who walk into a barber shop without an appointment.
In relation to the binomial distribution, if the number of trialsngets larger and larger as the probability of successesp
gets smaller and smaller, we obtain the Poisson distribution. The box below shows some of the basic characteristics
of the Poisson distribution.
Characteristics of the Poisson Distribution
- The experiment consists of counting the number of events that will occur during a specific interval of time or
in a specific distance, area, or volume. - The probability that an event occurs in a given time, distance, area, or volume is the same.
- Each event is independent of all other events. For example, the number of people who arrive in the first hour
is independent of the number who arrive in any other hour.
Poisson Random Variable
Mean and Variance
p(x) =
λxe−λ
x!x= 0 , 1 , 2 , 3 ,...
μ=λ
σ^2 =λwhere