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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:

Î¼ = Î£x * 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:

Î¼ = 0*0.18Â +Â 1*0.34Â +Â 2*0.35Â +Â 3*0.11Â +Â 4*0.02Â =Â Â **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, letâ€™s enter the data values and corresponding probabilities for a given probability distribution:

**Step 2: Multiply Values and Probabilities**

Next, weâ€™ll multiply the first number in the â€˜Valuesâ€™ column with the first number in the â€˜Probabilityâ€™ column:

Weâ€™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