Expected Value and Risk
Combine discrete outcomes with their probabilities.
Your numbers
Expected value
Use consistent units. The result follows the assumptions you enter.
Scenario comparison
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Formula
Use μ = Σpᵢxᵢ and V = Σpᵢ(xᵢ−μ)². xᵢ are outcome values and pᵢ are matching probability fractions totaling unity. μ is expected value and V is variance; standard deviation is its square root.
Combine discrete outcomes with their probabilities.
Worked example
- Outcome values
- 0, 10, 20
- Probabilities summing to 1
- 0.2, 0.5, 0.3
- Expected value
- 11
- Variance
- 49
- Standard deviation
- 7
Scope and limitations
Use consistent units. The result follows the assumptions you enter.
Inputs are checked for missing values and allowed ranges. A result outside the finite numeric range is not displayed. Rounding affects display, while the calculation uses the model’s numeric precision.
Check your units and assumptions before relying on a result. Changing a label does not convert a currency or physical unit.
Formula version: 5c0a6b45f063 · Example checked: