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Discrete Expected Value Calculator — result sheet
Calculate the expected value and variance of a discrete distribution from paired outcomes and probabilities.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: E(X)=Σxᵢpᵢ; Var(X)=Σ(xᵢ−E(X))²pᵢ.
The probability-weighted average gives the long-run center of the stated discrete model and the second result gives its variance.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Outcomes — Comma-separated finite outcomes.
- Probabilities — Comma-separated probabilities that sum to 1.
Worked example
| Input | Value |
|---|---|
| Outcomes | 0, 1, 2 |
| Probabilities | 0.2, 0.5, 0.3 |
Expected value =1.1; variance =0.49.
Assumptions and limits
- Outcomes and probabilities have matching lengths.
- Probabilities are nonnegative and sum to one within a small rounding tolerance.
- The distribution is discrete and complete; estimation from observed data is not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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