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
You have 2 free calculationss remaining
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.
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?
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
