Poisson Distribution Calculator

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. * 1

P(0; 4) =1
54.

P(0; 4) = 0.0183

In Microsoft Excel or , you write this function as =POISSON(0,4,FALSE)

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