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 step-by-step example shows how to calculate the expected value of a probability distribution on a TI-84 calculator.

**Step 1: Enter the Data**

First, we will enter the data.

Press Stat, then press EDIT. Then enter the data values in column L1 and their probabilities in L2:

**Step 2: Multiply the Two Columns**

Next, we will multiply columns L1 and L2.

Highlight the top of column L3 and type in the following formula: **L1 * L2**

Use these steps to enter this formula:

- Press Stat, then press 1.
- Press the multiplication x button.
- Press Stat, then press 2.

Once you press Enter, the following values will appear in column L3:

**Step 3: Find the Expected Value**

Lastly, use the following steps to find the expected value of the probability distribution:

- Press 2nd and then press MODE to return to the home screen.
- Press 2nd and then press STAT. Scroll over to “MATH” and then press 5.
- Press 2nd and then press 3.
- Press the ) button.

Once you press Enter, the expected value will be displayed:

The expected value turns out to be **1.45**.

Notice that this matches the expected value that we calculated by hand at the beginning of the article.

**Additional Resources**

How to Find Sample Variance on a TI-84 Calculator

How to Find Interquartile Range on a TI-84 Calculator

How to Calculate Relative Frequency on a TI-84 Calculator