Poisson Distribution Example (λ = 2 & x = 7)

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.

Calculation Summary
Success Rate (λ)	2
Random Variable (X)	7
P(X = 7)	0.0034
Mean (μ)	2
Variance (σ²)	2
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).

Work with step by step calculation :

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 λ^xx!

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

=17.32295040

= 0.0034

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.