Probability Distribution Calculator

Compute expected value, variance, and standard deviation from a discrete probability distribution. Enter values and their probabilities.

Enter values and probabilities.

Formulas

E(X) = Σ[x × P(x)]
Var(X) = Σ[(x − E(X))² × P(x)]
σ = √Var(X)
Example: Fair die: values 1–6, each P = 1/6
E(X) = 3.5 | Var(X) = 2.917 | σ = 1.708

FAQ

What is a probability distribution?

A discrete probability distribution assigns a probability to each possible outcome. The sum of all probabilities must equal 1.

Last updated: 2026-08-08