Everything You Need to Know About Poisson Distribution

Probability mass functions are used to describe discrete probability functions, while probability density functions describe continuous probability functions. The term probability functions cover both discrete and continuous distributions. In this tutorial, you will explore one such probability function: Poisson Distribution.

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What Is a Poisson Distribution?

The Poisson Distribution is a discrete probability distribution for the counts of events that occur randomly over a given period. Poisson Distribution is used in cases where any individual event's chances are very small. 

A Poisson Distribution can be used to calculate how likely it is that something will happen "X" a number of times. For example, suppose the average number of people who buy burgers from a Mcdonald's on a Sunday night at a single restaurant is 300. In that case, a Poisson distribution can answer questions such as, "what is the probability that more than 500 people will buy burgers?"

Conditions for Poisson Distribution

The Poisson condition is applicable only when the following conditions are satisfied:

  • An event can occur any number of times during a given time period.
  • The events are independent of each other. In other words, the probability of occurrence of one event does not affect the probability of occurrence of another event in the same time period.
  • The rate of occurrence is constant;  the rate does not change based on time.

Applications of Poisson Distribution

Here are some examples where Poisson distribution can be used on a day-to-day basis:

  • You can calculate the number of mutations on a DNA strand per unit of time.
  • The number of orders your firm receives for a particular product tomorrow.
  • The number of calls a hospital receives next week for emergency treatment.
  • The number of hungry persons entering KFC restaurants per day.

The Formula for the Poisson Distribution

The formula for the Poisson distribution is:



  • e is  = 2.7182
  • x is the number of occurrence
  • λ is the expected value of x 

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Example of Poisson Distribution

The average number of earthquakes in your city is 3 per year. What is the probability that exactly 5 earthquakes will occur in your city next year?

Step 1: Figure out the important values

  • λ = 3 (average number of earthquakes per year)
  • x = 5 (the number of earthquakes that might hit next year)
  • e = 2.71828

Step 2: Plug the values in the formula

f(x) = (2.71828 -3) * (35) / 5!

      = 0.0497 * 243 / 120

      = 0.100

The probability of having 5 earthquakes is 0.100, or 10% 

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In this "Poisson Distribution "tutorial, you learned about Poisson Distribution and its properties, along with an example to better understand the concept. 

If you are interested in learning more about probability distributions and related statistical concepts, you should look for Simplilearn's Postgraduate Program in Data Analytics. It is one of the most detailed online programs out there for this.  

If you have any questions for us, please mention them in our comments section, and we will get back to you.

About the Author

Aryan GuptaAryan Gupta

Aryan is a tech enthusiast who likes to stay updated about trending technologies of today. He is passionate about all things technology, a keen researcher, and writes to inspire. Aside from technology, he is an active football player and a keen enthusiast of the game.

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