Enter up to 10 possible outcomes (X values) and their corresponding probabilities P(X) to calculate the Expected Value E(X) of a random variable. The calculator sums each x·P(x) product and displays the result alongside a full breakdown table — perfect for statistics, decision analysis, and probability problems.
Expected Value E(X)
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Sum of Probabilities ΣP(X)
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Number of Outcomes
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Probability Valid (sums to 1)?
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The expected value E(X) is the long-run average outcome of a random variable if an experiment were repeated many times. It represents the weighted mean of all possible outcomes, where each outcome is weighted by its probability. For example, the expected value of a fair six-sided die is 3.5.
The expected value is calculated using the formula E(X) = x₁·P(x₁) + x₂·P(x₂) + … + xₙ·P(xₙ). You multiply each outcome value by its probability, then sum all those products together. This calculator does that automatically once you enter your outcomes and probabilities.
Yes — for a valid probability distribution, all P(X) values must sum to exactly 1. The calculator checks this for you and displays the sum of your probabilities. If the total is not 1, your distribution is incomplete or contains an error.
Absolutely. If the outcome values include negative numbers (such as financial losses), the expected value can be negative. This is common in gambling or investment contexts where some outcomes result in a net loss.
Expected value is used in statistics, economics, finance, game theory, and decision analysis. Whenever you face a decision with multiple possible outcomes — each with a known probability — computing E(X) helps you understand the average result you'd expect over many repetitions.
The expected value is a theoretical concept — the weighted average of all possible outcomes based on their probabilities. The sample mean, on the other hand, is calculated from actual observed data. As you collect more data, the sample mean tends to converge toward the expected value.
This calculator supports up to 10 outcome-probability pairs. If your random variable has fewer outcomes, simply leave the extra fields blank — the calculator will only use rows where both an X value and a P(X) value have been entered.
In sports betting, expected value tells you whether a wager is profitable over the long run. A positive EV bet means that, on average, you'd profit if you made the same bet many times. You calculate it by multiplying your potential win by the win probability and subtracting the potential loss multiplied by the loss probability.