What is poisson distribution explain the characteristics and formula?
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Answer:
Poisson Distributions
A Poisson probability 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.
Characteristics of a 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.
In a binomial distribution, if the number of trials, n, gets larger and larger as the probability of success, p, gets smaller and smaller, we obtain a Poisson distribution. The section below lists some of the basic characteristics of a Poisson distribution.
Answer:
Step-by-step explanation:
Poisson Distributions
A Poisson probability 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 are 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 a binomial distribution, if the number of trials, n, gets larger and larger as the probability of success, p, gets smaller and smaller, we obtain a Poisson distribution.
Characteristics of a 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.
The probability distribution, mean, and variance of a Poisson random variable are given as follows:
p(x)μσ2=λxe−λx!x=0,1,2,3,…=λ=λ
where:
λ= the mean number of events in the time, distance, volume, or area
e= the base of the natural logarithm