A History of the Central Limit Theorem
From Classical to Modern Probability Theory
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Focusing on the evolution of the central limit theorem, this study traces its history from 1810 to 1950, highlighting key developments in analytical probability theory and its methodologies, including characteristic functions and moments. It details how Laplace initially formulated the theorem as an approximation for the distributions of sums of independent random variables, set against the backdrop of classical probability's emphasis on specific applications and problems.