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Expected Value, Variance, and σ of a 3-Outcome Discrete Distribution Calculator

E[X] = Σ pᵢxᵢ; Var = Σ pᵢ(xᵢ − μ)² ; σ = √Var.

Given a discrete random variable with three outcomes x₁, x₂, x₃ and corresponding probabilities p₁, p₂, p₃ (summing to 1), compute the expected value E[X] = Σ pᵢxᵢ, the variance Var(X) = Σ pᵢ(xᵢ − E[X])², and the standard deviation σ = √Var(X).

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

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Formula

E[X] = Σ p·x; Var = Σ p·(x − μ)²; σ = √Var.

In depth

Given a discrete random variable with three outcomes x₁, x₂, x₃ and corresponding probabilities p₁, p₂, p₃ (summing to 1), compute the expected value E[X] = Σ pᵢxᵢ, the variance Var(X) = Σ pᵢ(xᵢ − E[X])², and the standard deviation σ = √Var(X).