Enter Number of Occurrences (n) Enter probability of success (p) Enter Number of successes (k) Enter Moment Number t (Optional)
       

Using a Poisson distribution with a probability of success of 0.4, calculate the Probability of having exactly 0 successes in 10 tries. Start with the Poisson Distribution formula below:
P(k; λ)  =  λk
  eλk!

Calculate λ
λ = p * n
λ = 0.4 * 10
λ = 4

Calculate k!:
k! = 0!
0! =
0! = 1

Calculate the probability:
P(k; λ)  =  λk
  eλk!

P(0; 4)  =  40
  2.7182818284(0!)

P(0; 4)  =  1
  54.598150033144 * 1

P(0; 4)  =  1
  54.598150033144

Excel or Google Sheets formula:

Excel or Google Sheets formula:=POISSON(0,4,FALSE)

P(0; 4) = 0.0183





What is the Answer?
P(0; 4) = 0.0183
How does the Poisson Distribution Calculator work?
Free Poisson Distribution Calculator - Calculates the probability of 3 separate events that follow a poisson distribution.
It calculates the probability of exactly k successes P(x = k)
No more than k successes P (x <= k)
Greater than k successes P(x >= k)
Each scenario also calculates the mean, variance, standard deviation, skewness, and kurtosis.
Calculates moment number t using the moment generating function
This calculator has 4 inputs.

What 2 formulas are used for the Poisson Distribution Calculator?

λ p * n
P(k; λ) = λk/eλk!

For more math formulas, check out our Formula Dossier

What 9 concepts are covered in the Poisson Distribution Calculator?

distribution
value range for a variable
event
a set of outcomes of an experiment to which a probability is assigned.
factorial
The product of an integer and all the integers below it
mean
A statistical measurement also known as the average
moment
a function are quantitative measures related to the shape of the functions graph
poisson distribution
a discrete probability distribution that is used to show how many times an event is likely to occur over a specified period.
probability
the likelihood of an event happening. This value is always between 0 and 1.
P(Event Happening) = Number of Ways the Even Can Happen / Total Number of Outcomes
standard deviation
a measure of the amount of variation or dispersion of a set of values. The square root of variance
variance
How far a set of random numbers are spead out from the mean
Poisson Distribution Calculator Video

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Calculate the mean μ and variance σ2:
In the poisson distribution, mean and variance = λ
μ = λ
μ = 4

σ2 = λ
σ2 = 4

Calculate the standard deviation σ:
σ = √σ2
σ = √4
σ = 2

Calculate Skewness:

Skewness  =  1
  λ

Skewness  =  1
  4

Skewness  =  1
  2

Skewness = 0.5

Calculate Kurtosis:

Kurtosis  =  1
  λ

Kurtosis  =  1
  4

Kurtosis = 0.25