This statement follows directly from considering the powers of a second- order characteristic function, then applying the Lévy continuity theorem.
This statement follows directly from considering the powers of a second- order characteristic function, then applying the Lévy continuity theorem. A theorem intimately related to this one uses the modulus of a normalized multi- fold convolution as a term in the bound of a third central moment; that theorem due to Berry and Esséen can be said to bound deviation from the result that this theorem guarantees. Conditions under which this statement holds are due to Feller and Lévy, Lindeberg, Gnedenko, Kolmogorov, and Lyapunov, who first relaxed its assumptions to independence and finite zeroth through second moments; previous versions of this theorem had additionally required identical distribution of the underlying variates. For ten points, identify this theorem that states that the distribution of a sample of independent random variables approaches a normal distribution with sample size.
This statement follows directly from considering the powers of a second- order characteristic function, then applying the Lévy continuity theorem.
the {central limit} theorem