What is Expected Value?

Expected value is a fundamental concept in probability theory and statistics. It represents the average outcome of an experiment if it is repeated many times. In other words, it’s the sum of each possible outcome multiplied by its probability of occurrence.

Expected value is crucial in various fields, including finance, economics, decision theory, and game theory, as it helps predict long-term results and make informed decisions based on probabilistic outcomes.

How to Use the Expected Value Calculator?

1. Entering Data

• In the “Outcome (x)” column, enter the numerical value of a possible outcome. This could be a monetary amount, a score, or any other quantifiable result.
• In the “Probability P(x)” column, enter the probability of that outcome occurring. This should be a decimal between 0 and 1, where 0 means impossible and 1 means certain.

2. Adding More Outcomes

• If your scenario has multiple possible outcomes, click the “Add Row” button to create additional input rows.
• Continue entering outcomes and their probabilities in these new rows.
• If you’ve added too many rows or need to remove an outcome, use the “Remove” button next to the respective row.

3. Calculating the Expected Value

Once you’ve entered all outcomes and probabilities, click the “Calculate Expected Value” button at the bottom of the table.

The calculator will display the expected value in the results section below the table.

4. Formula Reference

The formula E(X) = Σ(x * P(x)) is displayed at the bottom for reference, where X is the random variable, x represents each possible outcome, and P(x) is the probability of that outcome.

By following these steps, users can effectively utilize the Expected Value Calculator to analyze various probabilistic scenarios and make data-driven decisions based on the expected outcomes.