# Poisson Distribution

## Poisson Distribution

• calculating randomly scattered events in time or in space
Examples
• number of road accidents in given period
• goals scored in a soccer match
• number of Losses/Claims occurring in a given period
• number of customers calling in a day

## Formula

• In order to apply the Poisson distribution, the various events must be independent.

General formula of Poisson distribution is:

``` e is the base of natural logarithms (2.7183)
μ is the mean number of "successes"
x is the number of "successes" in question
```

## Example

Suppose you knew that the mean number of customer calls to your company on a weekday is 8.

• What is the probability that on a given weekday there would be 11 calls?
• This problem can be solved using the following formula based on the Poisson distribution:
``` =POISSON(11,8,false)
```

since the mean is 8 and the question pertains to 11 calls.

• The mean of the Poisson distribution is μ.
• The variance is also equal to μ.
• Thus, for this example, both the mean and the variance are equal to 8.

# Quiz

<quiz display=simple>

{The mean number of defective products produced in a factory in one day is 21. What is the probability that in a given day there are exactly 12 defective products?

|type="{}"} { 0.012 | .012 }

{