# Poisson Probability Distribution

Calculator

## Poisson Probability Distribution Formula

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 variable2. 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.