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An Insight into the Law of Large numbers
The Law of the Large Number was proven for the first time in 1713 by Swiss Mathematician Jakob Bernoulli. It is a theorem in Statistics that states as the sample size of identically distributed and randomly generated variables grow, the sample mean gradually gets closer to the theoretical mean.
Bernoulli and his contemporaries were trying to develop a probability theory for games of chance, where Bernoulli envisaged a continuous repetition of a game of chance with only two possible outcomes: a win or a loss! Considering the probability of winning to be ‘p’, Bernoulli considered that fraction of times such a game could be won when played repeatedly, and imagined this fraction will gradually approach ‘p’. Finally, he proved this theorem precisely, that when the repetition continues indefinitely, the probability of the given fraction at any distance from ‘p’ eventually approaches 1.
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