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Nov 4, 2024 · law of large numbers, in statistics, the theorem that, as the number of identically distributed, randomly generated variables increases, their sample mean (average) approaches their theoretical mean. The law of large numbers was first proved by the Swiss mathematician Jakob Bernoulli in 1713.
5 days ago · This distribution was derived by Jacob Bernoulli. He considered the case where p = r/(r + s) where p is the probability of success and r and s are positive integers. Blaise Pascal had earlier considered the case where p = 1/2, tabulating the corresponding binomial coefficients in what is now recognized as Pascal's triangle. [45]
Nov 9, 2024 · Jacob Bernoulli is known for his numerous contributions to calculus, and along with his brother Johann, was one of the founders of the calculus of variations.
3 days ago · The Swiss mathematician Jakob Bernoulli (1654–1705) was the first to realize the existence of a single sequence of constants B 0, B 1, B 2,... which provide a uniform formula for all sums of powers.
3 days ago · The calculus of variations (or variational calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions to the real numbers.
Oct 23, 2024 · Swiss mathematician Jakob Bernoulli, in a proof published posthumously in 1713, determined that the probability of k such outcomes in n repetitions is equal to the kth term (where k starts with 0) in the expansion of the binomial expression (p + q) n, where q = 1 − p.
Nov 5, 2024 · Jacob Bernoulli's Ars Conjectandi, published posthumously in Latin in 1713 by the Thurneysen Brothers Press in Basel, is the founding document of mathematical probability. Here, Edith Dudley Sylla offers the first complete English translation of this monumental work.
