Poisson Distribution

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Poisson Distribution

Poisson pmf.svg

  • calculating randomly scattered events in time or in space
  • number of road accidents in given period
  • goals scored in a soccer match
  • number of Losses/Claims occurring in a given period
  • number of customers calling in a day


  • In order to apply the Poisson distribution, the various events must be independent.

General formula of Poisson distribution is:

e is the base of natural logarithms (2.7183)
μ is the mean number of "successes"
x is the number of "successes" in question


Suppose you knew that the mean number of customer calls to your company on a weekday is 8.

  • What is the probability that on a given weekday there would be 11 calls?
  • This problem can be solved using the following formula based on the Poisson distribution:
In a spreadsheet

since the mean is 8 and the question pertains to 11 calls.

  • The mean of the Poisson distribution is μ.
  • The variance is also equal to μ.
  • Thus, for this example, both the mean and the variance are equal to 8.


<quiz display=simple>

{The mean number of defective products produced in a factory in one day is 21. What is the probability that in a given day there are exactly 12 defective products?

|type="{}"} { 0.012 | .012 }


Answer >>


0.012 can be obtained using the formula.


{Which of these can be computed using Poisson distribution? |type="[]"} -average waiting time between phone calls +number of people killed accidentally by horse kicks

{Which of these can be computed using Poisson distribution? |type="[]"} +number of enquiries via online form in a month -probability of selecting a person over 2 meter high