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), variance2) & 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 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. 