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On the law of large numbers
At the turn of17th century and18th century, many mathematicians engaged in the study of probability. Bernoulli's masterpiece Guessing is a great achievement, in which Bernoulli's theorem is the earliest form of large number theorem, and the first limit theorem in probability theory is "the frequency tends to be more stable in repeated experiments". After that, Dimover and Simpson made great progress. /kloc-In the 8th century, Buffon, a French natural philosopher, introduced the "needle throwing problem" into probabilistic arithmetic experiments. He drew many parallel straight lines with equal distance on a piece of paper. He threw small needles on the paper at will, and he threw them 22 12 times. As a result, 704 * * * intersects with parallel straight lines. The ratio of the total number 22 12 to the intersection number 704 is 3. 142. Buffon's more general result is that if the distance between two parallel lines on the paper is, the length of small needles is, the number of needles is, and the number of needles intersecting with parallel lines is, then when it is quite large, there is:. The numerical value is calculated in the same way later. The most amazing is the Italian mathematician Lazzerini. In 190 1, he claimed that the value obtained by repeated needle injection experiments was 3. 14 15929. Compared with the exact value of, it doesn't differ until seven decimal places! Using such ingenious methods to get such high and accurate values is the real natural creation! 19th century, probability theory has made great progress. Laplace's classic book Analytic Probability Theory summarizes the research of probability theory in this era and puts forward the classical definition of probability. Gauss laid the foundation of least square method and error theory. Poisson generalized the law of large numbers and introduced a very important Poisson distribution. Chebyshev and his student Markov founded the law of large numbers and Markov chain respectively. In 1930s, Kolmo Golov of the Soviet Union put forward an axiomatic system of probability theory based on Lebesgue measure theory, which had great influence. With the development of society and the progress of science, probability theory, with its unique charm, encourages more and more scientific and technological workers to continuously promote its application, development and innovation. It is a new subject in mathematics, and it has penetrated into other branches of mathematics, resulting in stochastic differential equations, stochastic geometry and other theories. Probability theory is widely used, except natural science, social and economic statistics has become an independent branch; Combined with other disciplines, it forms marginal disciplines such as biostatistics, statistical prediction, statistical physics and econometric history.