A probability distribution tells us the probability that a random variable takes on certain values.

For example, the following probability distribution tells us the probability that a certain soccer team scores a certain number of goals in a given game:

To find the **expected value** of a probability distribution, we can use the following formula:

μ = Σx * P(x)

where:

- x: Data value
- P(x): Probability of value

For example, the expected number of goals for the soccer team would be calculated as:

μ = 0*0.18 + 1*0.34 + 2*0.35 + 3*0.11 + 4*0.02 = **1.45** goals.

The following example provides a step-by-step example of how to calculate the expected value of a probability distribution in Excel.

**Step 1: Enter the Data**

First, let’s enter the data values and corresponding probabilities for a given probability distribution:

**Step 2: Multiply Values and Probabilities**

Next, we’ll multiply the first number in the ‘Values’ column with the first number in the ‘Probability’ column:

We’ll then copy and paste this formula down to every cell in column C:

**Step 3: Calculate Expected Value**

Lastly, we can calculate the expected value of the probability distribution by using **SUM(C2:C10)** to sum all of the values in column C:

The expected value for this probability distribution is **3.3**.

**Additional Resources**

The following tutorials explain how to calculate other descriptive statistics in Excel:

How to Find Mean, Median & Mode in Excel

How to Calculate the Interquartile Range in Excel

How to Calculate the Coefficient of Variation in Excel