Table of Contents
A probability distribution tells us the probability that a 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.