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Statistics result
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Connecting outcomes, probabilities, and long-run value. A discrete random variable assigns a numerical value to every possible outcome. Its distribution supports expected value and variance, but an expectation is a long-run average—not a guaranteed single outcome.
1Pair every value with its probability2Confirm probabilities form a complete model3Weight values or squared deviations and add
Probability rule
E(X)=Σxᵢpᵢ.
Every probability must remain between 0 and 1, and overlapping regions must be jointly feasible. The calculator rejects combinations that violate the stated model.
How to interpret it
Expected value is a long-run average, not a guarantee for any single outcome.
Model boundary: Outcome and probability lists must align, and probabilities must total one within rounding tolerance.
Quick guide
How to use this calculator
Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
Read the result together with its assumptions and interpretation. Statistical output summarizes uncertainty under a model; it does not repair biased data or establish causation.
Calculation method
How the expected value calculator works
E(X)=Σxᵢpᵢ.
Expected value is a long-run average, not a guarantee for any single outcome.
Worked example
Expected Value example
Outcomes 0 and 10 with probabilities 0.7 and 0.3 have expected value 3.
E(X)=Σxᵢpᵢ.
Supported inputs
Precision and limits
Model and design
Outcome and probability lists must align, and probabilities must total one within rounding tolerance.
Numerical scope
Inputs use double-precision numerical methods with guarded domains. Datasets accept up to 10,000 finite plain-decimal values. Extremely large parameters or probabilities deep in a numerical tail may require specialist statistical software.
Interpretation
Expected value is a long-run average, not a guarantee for any single outcome.
Decision boundary
The calculator does not validate how data were collected, diagnose dependence or bias, choose a scientifically meaningful effect, or replace review by a qualified statistician for consequential research, medical, regulatory, safety, or policy decisions.
Privacy
Entered values and calculated results stay in this browser and are not sent to an analytics service.
