# 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* (σ^{2}) & *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 (σ^{2}) | 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

^{x}x!

P(X = 7) =e

^{-2}2

^{7}7!

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}2

^{7}5040

=0.1353 x 1285040

=17.32295040

= 0.0034

P(X = 7) = 0.0034

Mean (μ) = 2

Variance (σ

^{2}) = 2

Standard deviation (σ) = 1.4142

Thus, the probabilty of success P(x) is 0.0034 for λ = 2, x = 7.

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