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math.probability-expected-value Calculator
Calculates expected value and variance of a discrete probability distribution from a table of outcomes and their probabilities. Expected value is the long-run average outcome — it's what makes casino odds profitable for the house and negative for the player.
Inputs
X1
Reference formula or conversion factor shown for context.
P1
Reference formula or conversion factor shown for context.
X2
Reference formula or conversion factor shown for context.
P2
Reference formula or conversion factor shown for context.
X3
Reference formula or conversion factor shown for context.
P3
Reference formula or conversion factor shown for context.
Results
E(X)
Reference formula or conversion factor shown for context.
Var(X)
Reference formula or conversion factor shown for context.
\u03c3
Reference formula or conversion factor shown for context.
std dev
Standard deviation -- the average spread of values around the mean. In a normal distribution: 68% within 1 SD, 95% within 2 SD.