This tutorial shows how to compute a probability density function, a cumulative distribution function, or an inverse cumulative distribution function in Excel using the XLSTAT software.

## What is a probability distribution?

A probability distribution is a special type of function known as a measure in mathematics. It allows to relate random events to their probability. A random event can be the occurrence of a 2 when throwing a dice, the arrival of two customers to a post office at the same time, drawing a King from a well-shuffled deck of card, etc.

A large number of probability distributions have been developed to describe particular situations where randomness occurs. Randomness is a representation of the unknown or imperfect knowledge. When you roll a dice for example, a perfect understanding of your tossing movement would presumably allow you to know when, where, and in what position the dice might stop. However, figuring out how the dice should be thrown to replicate the exact same result would so complex that it is preferable to estimate that each face has a certain probability and that the occurrence of an event is random. Click here to read more.

## Goal of this tutorial

One counts the number of emails received at work each day during a certain period. Let’s assume that the occurrence of this event follows a **Poisson distribution with an average rate** (labda) equal to 5.

Based on this information, we want to compute:

- The probability they will receive 10 emails a day.
- The probability they may receive between 3 and 6 emails a day.
- Given a probability of occurrence equal to 0.8, how many emails are they likely to receive within a day?

We will also visualize the probability density function.

## Setting up the Probability Calculator in XLSTAT

Select the **XLSTAT / Mathematical tools / Probability Calculator** command (see below).

The **Probability** **Calculator** dialog box appears.

On the left-hand side of the dialog box, choose your **distribution**, enter the **parameters **and choose whether you want to compute the density function, the cumulative distribution function (CDF) or the inverse CDF.

In the middle part of the dialog box, choose where you want to display the output and visualize the computed probability within the interface.

On the right-hand size of the dialog box, visualize the distribution function.

Start by selecting the **Poisson** distribution from the drop down list.

Then enter the value 5 in the **lambda** field which correponds to the average number of received emails per day. Lambda is the **event** **rate**, also called the **rate** **parameter**.

### What is the probability to receive 10 emails in a day?

### What is the probability to receive between 3 and 6 emails in a day?

### Which is the number of received emails in a day such as the probability to receive this amount is 0.8?