Poisson Distribution Example for λ = 2 & x = 7
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 = 2, x = 7 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.
|Success Rate (λ)||2|
|Random Variable (X)||7|
|P(X = 7)||0.0034|
|Standard Deviation (σ)||1.4142|
Solved Example Calculation for λ = 2 & x = 7
This below solved example for Poisson probability distribution with step by step calculation shows how the input parameters λ = 2 & x = 7 are being used in the Poisson distribution formula to find the probability of success P(x).
step 1 Address the formula, input parameters and values
Success Rate (λ) = 2
Random Variable (x) = 7
step 2 Substitute success rate & random variable in the below Poisson probability distribution formula
P(X = x) =e-λ λxx!
P(X = 7) =e-2 277!
step 3 To find the factorial for 7
7! = 1 x 2 x 3 x . . . . x 6 x 7
7! = 5040
step 4 Simplify the above expression
P(X = 7) =e-2 275040
=0.1353 x 1285040
P(X = 7) = 0.0034
Mean (μ) = 2
Variance (σ2) = 2
Standard deviation (σ) = 1.4142
Thus, the probabilty of success P(x) is 0.0034 for λ = 2, x = 7.