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Poisson distribution facts for kids

Kids Encyclopedia Facts
Poisson distribution PMF
Typical Poisson distribution

The Poisson distribution is a special idea in probability and statistics. It helps us understand how likely it is for a certain number of events to happen within a specific time or space. This idea was discovered by a French mathematician named Siméon Denis Poisson in 1838.

Imagine you are counting things that happen randomly and independently. The Poisson distribution can help you predict how many times those events might occur. For this to work, the events must not affect each other. Also, you need to know the average number of times the event usually happens. This average is often shown by the Greek letter \lambda (lambda).

More specifically, if a random variable X follows the Poisson distribution with an average rate \lambda, then the probability of seeing a certain number of events (x) can be found using this formula:

P(X=x)=\frac{e^{-\lambda} \lambda^x}{x!} for x = 0, 1, 2, \ldots

This formula helps scientists and statisticians calculate the exact chance of seeing 0 events, 1 event, 2 events, and so on.

What it Helps Predict

The Poisson distribution is useful for predicting many real-world events. It works best when events happen randomly and independently over a set period or area.

Here are some examples of what the Poisson distribution can help predict:

  • The number of cars that drive past a certain point on a road in an hour.
  • How many phone calls a customer service center gets in one minute.
  • The number of light bulbs that stop working in a building over a month.
  • How many errors might appear in a computer system during a day.
  • The number of small changes (called mutations) in a piece of DNA after being exposed to something like radiation.
  • The number of insurance claims a company receives in a week.

For example, imagine someone keeps track of how much mail they get each day. They might notice they receive an average of 4 letters daily. If getting one letter doesn't change when the next one arrives, then the number of letters they get each day likely follows a Poisson distribution. This means the letters arrive independently from many different sources.

Related pages

Images for kids

  • Chewing gum on a sidewalk in Reykjavík

    Chewing gum on a sidewalk. The number of chewing gums on a single tile is approximately Poisson distributed.

See also

Kids robot.svg In Spanish: Distribución de Poisson para niños

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Poisson distribution Facts for Kids. Kiddle Encyclopedia.