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Cumulative Poisson Distribution Tutorial

  


Cumulative Poisson Distribution
Definition:

   A cumulative poisson distribution is used to calculate the probability of getting atleast n successes in a poisson experiment. Here, n is the poisson random variable which refers to the number of success.

Formula:

   P(x < n) = P(x = 0) + P(x = 1) + ... + P(x = n)

  where, P(x = 0) and P(x = 1) is calculated using poisson distribution formula.

Example:

  Consider, in an office 2 customers arrived today. Calculate the possibility for atleast 3 customers to be arrived on tomorrow.

  where, λ=2 , e=2.718 and x=3.

  P(x < 3) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3)
              = e-2 λ0 / 0! + e-2 λ1 / 1! + e-2 λ2 / 2! + e-2 λ3 / 3!
              = 0.135 + 0.271 + 0.271 + 0.18
              = 0.857.

  Hence there are atleast 85.7% possibilities for atleast 3 customers to be arrived on tomorrow.




This tutorial will guide you to calculate the cumulative poisson distribution.

Related Topics:
>> What is Poisson distribution?

Related Calculator:
>> Calculate Poisson distribution online