Poisson Distribution Example for λ = 3 and x = 11
The below summary and example workout with step by step calculation shows how to estimate P(x), mean (μ), variance (σ2) and standard deviation (σ) of Poisson probability distribution for the input values λ = 3, x = 11 may be helpful for beginners to learn how the input parameters are being used in the Poisson formula in probability and statistical experiments or useful for grade school students to solve such similar worksheet or homework problems efficiently.
| Calculation Summary | |
|---|---|
| Success Rate (λ) | 3 |
| Random Variable (X) | 11 |
| P(X = 11) | 0.0002 |
| Mean (μ) | 3 |
| Variance (σ2) | 3 |
| Standard Deviation (σ) | 1.7321 |
Solved Example Calculation for λ = 3 and x = 11
This below solved example for Poisson probability distribution with step by step calculation shows how the input parameters λ = 3 and x = 11 are being used in the Poisson distribution formula to find the probability of success P(x).
Work with step by step calculation :
step 1 Address the formula, input parameters and values
Success Rate (λ) = 3
Random Variable (x) = 11
step 2 Substitute success rate and random variable in the below Poisson probability distribution formula
P(X = x) =e-λ λxx!
P(X = 11) =e-3 31111!
step 3 To find the factorial for 11
11! = 1 x 2 x 3 x . . . . x 10 x 11
11! = 39916800
step 4 Simplify the above expression
P(X = 11) =e-3 31139916800
=0.0498 x 17714739916800
=8819.629839916800
= 0.0002
P(X = 11) = 0.0002
Mean (μ) = 3
Variance (σ2) = 3
Standard deviation (σ) = 1.7321
Thus, the probabilty of success P(x) is 0.0002 for λ = 3, x = 11.
step 1 Address the formula, input parameters and values
Success Rate (λ) = 3
Random Variable (x) = 11
step 2 Substitute success rate and random variable in the below Poisson probability distribution formula
P(X = x) =e-λ λxx!
P(X = 11) =e-3 31111!
step 3 To find the factorial for 11
11! = 1 x 2 x 3 x . . . . x 10 x 11
11! = 39916800
step 4 Simplify the above expression
P(X = 11) =e-3 31139916800
=0.0498 x 17714739916800
=8819.629839916800
= 0.0002
P(X = 11) = 0.0002
Mean (μ) = 3
Variance (σ2) = 3
Standard deviation (σ) = 1.7321
Thus, the probabilty of success P(x) is 0.0002 for λ = 3, x = 11.
