# POISSON

The `POISSON` function returns the Poisson distribution probability density function, which is used to show the probability of a certain number of events occurring in a fixed interval of time or space. It takes in the values for the number of events (x), the mean (mean), and a boolean for whether or not to return the cumulative distribution (cumulative).

## Usage

Use the `POISSON` formula with the syntax shown below, it has 2 required parameters and 1 optional parameter:

Parameters:
1. x (required):
The number of events to evaluate the probability for.
2. mean (required):
The mean number of events that occur in the given interval.
3. cumulative (optional):
A boolean that determines whether to return the cumulative distribution function or probability density function. If omitted or false, it will return the probability density function.

## Examples

Here are a few example use cases that explain how to use the `POISSON` formula in Google Sheets.

### Estimating the probability of an event

Suppose that you know that a certain number of events occur every day on average, and you want to know the probability of a certain number of events occurring in a day. You can use the `POISSON` function to calculate this probability.

### Analyzing traffic congestion

You can use the `POISSON` function to analyze traffic congestion in a particular area. By estimating the average number of vehicles that pass through the area in a given time interval, you can use the function to estimate the probabilities of different levels of congestion.

The `POISSON` function is also used in nuclear physics to model the probability of radioactive decay events occurring in a given time interval.

## Common Mistakes

`POISSON` not working? Here are some common mistakes people make when using the `POISSON` Google Sheets Formula:

### Using a negative value for x

The `POISSON` function requires that the value of `x` be a non-negative integer. If a negative value is used, the function will return an error.

### Using a negative value for mean

The `POISSON` function requires that the value of `mean` be a positive number. If a negative value is used, the function will return an error.

### Forgetting to set the cumulative argument

The `POISSON` function requires that the `cumulative` argument be set to either `TRUE` or `FALSE`. If this argument is omitted or misspelled, the function will return an error.

The following functions are similar to `POISSON` or are often used with it in a formula:

• `BINOM.DIST`

The `BINOM.DIST` function returns the probability of a certain number of successes in a fixed number of trials given a probability of success in each trial. It is most commonly used in statistical analysis and hypothesis testing. The function can calculate either the probability mass function (PMF) or the cumulative distribution function (CDF) depending on the value of the `cumulative` parameter.

• `NORM.DIST`

The `NORM.DIST` formula is a statistical function that returns the normal distribution of a specified variable. It is used to determine the probability of a random variable falling within a specified range of values. This function is commonly used in finance and scientific research.

• `EXPON.DIST`

The EXPON.DIST function returns the exponential distribution of a specified random variable, x, given a specified lambda, LAMBDA. The exponential distribution is commonly used to model the time between events in a Poisson process. The function returns the probability density function or the cumulative distribution function of the exponential distribution depending on whether the cumulative argument is set to TRUE or FALSE. This function is useful for analyzing reliability data and can be used to determine the probability that a component will fail before a certain time.

You can learn more about the `POISSON` Google Sheets function on Google Support.