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Free expected value calculator for discrete probability distributions. Enter outcomes and probabilities to compute E[X], variance, and standard deviation for decision and risk analysis.
Last updated: April 20, 2026
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Expected value E[X]
55.0000
Variance Var(X)
1225.0000
Standard deviation
35.0000
Probability total
1.0000
Interpretation
Expected value is 55.0000. Probabilities sum to 1.
Formula:
E[X] = Σ xᵢpᵢ
Var(X) = Σ (xᵢ - E[X])²pᵢ
Formula
E[X] = Σ xᵢpᵢ
Variance
Var(X) = Σ(xᵢ - μ)²pᵢ
Input modes
Decimal / Percent
Outcomes: 0, 50, 100 | Probabilities: 0.2, 0.5, 0.3
Expected value
55.00
Standard deviation
35.00
The calculator multiplies each outcome by its probability and sums across all outcomes to compute expected value. It then calculates variance and standard deviation for spread/risk around that expected center.
E[X] = Σ xᵢpᵢVar(X) = Σ (xᵢ - E[X])²pᵢSD = √Var(X)If probabilities do not sum to exactly 1, they are normalized to preserve relative weights.
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Suggested hashtags: #ExpectedValue #Probability #Statistics #RiskAnalysis #Math