Expected Value E(X) Calculator
Local ProcessingCalculate expected mathematical payoff E(X) = Σ (xᵢ × P(xᵢ)) from outcomes and probability weights.
How It Works & Processing Standards
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Expected value = Σ(outcome × probability) — what you get on average if you repeat the choice many times.
How to Use Expected Value E(X) Calculator
- 1Enter outcomesEach possible result. Losses are negative.
- 2Enter probabilitiesIn the same order, each from 0 to 1. They must add up to 1.
- 3Read the resultPositive means a gain on average, negative a loss.
Examples
Event entry gain or loss
Input: Outcomes 10000, 0, -5000 / probabilities 0.2, 0.5, 0.3
Result: 500
Expected die roll
Input: Outcomes 1–6 / each 1/6 as a decimal
Result: 3.4999999995
Common Use Cases
- Average gain or loss of a prize event or game
- Comparing expected returns across scenarios
- Checking probability homework
Frequently Asked Questions (FAQ)
What if the probabilities do not add up to exactly 1?
Small rounding is accepted, but a sum far from 1 is flagged. Probabilities like 1/6 typed as decimals shift the result slightly, as in 3.4999999995.
Is a positive expected value always a win?
It is the average over many repeats; any single try can still lose.