Poisson Distribution Example for λ = 3 & x = 11
The below summary & example workout with step by step calculation shows how to estimate P(x), mean (μ), variance (σ2) & standard deviation (σ) of Poisson probability distribution for the input values λ = 3, x = 11 may helpful for beginners to learn how the input parameters are being used in the Poisson formula in probability & 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 & x = 11
This below solved example for Poisson probability distribution with step by step calculation shows how the input parameters λ = 3 & 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 & 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 & 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.
