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Poisson Distribution

The Poisson Distribution is a discrete distribution named after French mathematician Simeon-Denis Poisson.

Unlike the binomial distribution that has only two possible outcomes as a success or fail, this distribution focuses on the number of discrete occurrences over a defined interval.

The Poisson formula describes rare events and is also referred to as the law of improbable events. The formula is shown below to calculate the probability of occurrences over an interval.

Poisson Formula

The Poisson distribution exhibits the following:

discrete distribution

occurrences are independent of each other

occurrences range from 0 to infinity in an interval

describes rare events

describes discrete occurrences of defined interval

expected number of occurrences must be constant in a Poisson experiment, this is the value of lambda.

Examples of Poisson distribution may be found in the following:

number of customers per minute in bookstore

number of transactions per hour at a bank

number of telephone calls made long distance per day at work

number of cracks in a windshield after installation

number of cars passing through an intersection per day

number of late shipments per 1,000 shipments made

number of pieces scrapped per 1,000,000 pieces produced

number of planes arriving per hour at airport

number of vacant houses per county in a state

Example

A new website has an average random hit rate of 2.9 unique visitors every 4 minutes. What is the probability of getting exactly 50 unique visitors every hour?

Given information

Example of Poisson Distribution

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