History of the Birth of the Central Limit Theorem

• In the late 17th century, Newton (Sir Isaac) and Leibniz (German newspaper) independently formulated the integral

• 1730 de moivre was [Sterling’s formula https://ja.wikipedia.org/wiki/%E3%82%B9%E3%82%BF%E3%83%BC%E3%83%AA%E3%83%B3%E3%82%B0%E3%81%AE%E8%BF%91%E 4%BC%BC]Stirling’s formula Found

• In 1773, de Moivre formulated normal distribution as an approximation of [binomial distribution

  • Binomial distribution becomes normal with n → ∞
    • Laplace. elaborated, this approximation is called [Laplace’s theorem

• 1838 Poisson distribution, mathematician Simeon Denis Poisson.

  • When p is small enough, the binomial distribution can be approximated by a Poisson distribution

• 1922 Central Limit TheoremCentral Limit Theorem

Probability distribution

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