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Expected Value Calculator

Online expected value: from the distribution table E(X)=Σxᵢpᵢ.

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E(X)=Σxᵢpᵢ
Value
Probability

📖 Tutorial | Expectation

1. Definition
For a discrete random variable, E(X)=Σxᵢpᵢ, the probability-weighted average.
2. Formula & Notation
x,pValues, probabilities
3. Properties & Laws
  • Weighted mean;
  • Linear E(aX+b)=aE(X)+b;
  • Probabilities sum to 1;
  • Long-run average.
4. Steps
  1. Enter values and probabilities;
  2. Click "Expectation";
  3. Or click "Load Example".
5. Worked Examples
Example: 1·0.2+2·0.3+3·0.5: E=2.3.
6. Common Pitfalls
Weighted, not simple average;
Probabilities sum to 1;
Include all values.

❓ FAQ | Expectation

Expectation?
Weighted mean.
Formula?
Σx p.
Linear?
aE+b.
Prob sum?
1.
Example?
2.3.
Attained?
Not necessarily.