where μ = IE(X) ∈ IR and σ = var(X) > 0 are the mean and variance of X . We write X ∼ N (μ, σ). Note that X = σZ + μ for Z ∼ N (0, 1) (called standard Gaussian) and where the equality holds in distribution. Clearly, this distribution has unbounded support but it is well known that it has almost bounded support in the following sense: IP(|X −μ| ≤ 3σ) ≃ 0.997… (More)

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