PROOF 197

Prove.

With many repetitions the average approaches the expected value

On a probability space.

Definition D1

Let X₁, X₂, … be mutually independent, identically distributed random variables with E(Xᵢ) = μ and Var(Xᵢ) = σ² < ∞. Define the sample mean X̄ₙ = (X₁ + … + Xₙ)/n.

Proof.

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