# Central Limit Theorem And The Distribution Of The Number Of Heads Essay

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Central Limit Theorem Abraham De Moivre, a French mathematician, published an article 1733, which he used the normal distribution to approximate the distribution of the number of heads resulting from many tosses of a coin. His work was nearly forgotten until another French mathematician can along who name was Pierre-Simon Laplace. Laplace explained De Moivre’s findings by approximating the binomial distribution with normal distribution. In 1785 Laplace introduced the characteristic functions which were the sum of error distribution, which took the value of -1 and +1 with equal probabilities. This work helped Laplace with the concept of the CLT, which he wrote a paper on in 1810. Sime`on Denis Poisson tried to provide an exact mathematical analysis to Laplace theorem. Poisson provided proof of the CLT for identically distributed variables. At the end of the 19th century mathematician was changing their train of thoughts from computational to fundamental (“pure” math) mathematic. Dirichlet and Bessel followed in the footsteps of Laplace and Poisson. They introduced the “discontinuity factors”, which proved Poisson’s equation for an arbitrary value of n. Cauchy’s was the first mathematician to consider probability theory as “pure” mathematics. He found an upper bond to the difference between the exact value and the approximation and then specified conditions for those bound to tend to zero. The problem with his theorem was that it was not proven for distributions with