# Poisson Probability Distribution Calculator

λ=
x=

Solution

P(x)=

## Poisson Probability Distribution Formula

$\LARGE P(x)=\frac{\lambda ^xe^{-\lambda}} {x!}$

λ = the mean number of occurrences in the interval
e = approximately 2.71828
x = the number of occurrences we wish to evaluate

### Poisson Probability Distribution Conditions

1. x is a discrete random variable
2. The occurrences are random
3. The occurrences are independent

### Sample Poisson Probability Distribution Problem

A vending machine in an office stops working an average of 3 times per a month. What is the probability that the vending machine will break exactly 2 times in the next month?

In this problem, λ = 3 and x = 2. The answer is .224. The probability of the machine breaking 2 times is .224.

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