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math.expected-value-discrete Calculator
Calculates expected value, variance, and standard deviation of a discrete probability distribution from a table of outcomes and their probabilities. The expected value is the probability-weighted average outcome — a $5 expected value means winning $5 on average per trial over many repetitions.
Inputs
Outcome1
Reference formula or conversion factor shown for context.
Prob1 Pct
Reference formula or conversion factor shown for context.
Outcome2
Reference formula or conversion factor shown for context.
Prob2 Pct
Reference formula or conversion factor shown for context.
Outcome3
Reference formula or conversion factor shown for context.
Prob3 Pct
Reference formula or conversion factor shown for context.
Results
expected value E[X]
The computed numeric or monetary value.
variance σ²
Standard deviation squared — average squared deviation from the mean. Essential for ANOVA, regression, and many statistical tests, though the squared units make it less intuitive directly.
standard deviation σ
Average spread of values around the mean. In a normal distribution: 68% within ±1 SD, 95% within ±2 SD, 99.7% within ±3 SD. Large SD = widely spread data; small SD = tightly clustered.
probability sum
The arithmetic total of all input values.
E[X] = Σ xᵢ·pᵢ
Reference formula or conversion factor shown for context.