Probability theory began in17th century. Cardano, Fei Erman, Pascal and others were early researchers in probability theory. They mainly study the probability-chance of independent random events, and discuss the "chance" in the process of gambling and lottery winning. People gradually demand to solve the probability or expectation problem related to a large number of event sets. For example, if the total number of lottery tickets is large and it is known that each lottery ticket has an equal chance of winning, what is the winning probability of drawing 1 000 and 1 000 lottery tickets? People want to know how many lottery tickets they should buy at least if the probability of winning is to reach 90%. Consider a series of random events (such as random coin toss). The probability of one event (such as head-on flip) is p, n represents the total number of all random events, and m is the number of one event. What is the law of the ratio of the number of occurrences (m) of this event to the number of all events (n)? This is a very important problem in17th century probability theory.
17 13 years, Jacob Bernoulli's posthumous work "Ars Conjecture" was published, which shows that after repeated experiments, the above probability is 0.9999; If you add 5708 tests, that is, 36966 tests, the above probability is 0.99999, and so on. Therefore, Jacob Bernoulli pointed out: "Through infinite experiments, we can finally correctly calculate the probability of anything and see the order of things from accidental phenomena." However, he did not express the order in this accidental phenomenon. The work was done by de Moif.
Before the publication of Jacob Bernoulli's Conjecture, De Moivre made extensive and in-depth research on probability theory. 171/kloc-0 published "De mensure sortis" in Philosophical Transactions of the Royal Society, which was translated into "Opportunism" when it was published in English in 17 18. He didn't discuss the problems discussed by Jacob Bernoulli in his book, but when The Theory of Opportunity was reprinted in 1738, De Moivre gave an important solution to these problems. It is often said that there are three landmark works in the early history of probability, among which De Moivre's Theory of Opportunity is one, and the other two are Bo's Theory of Speculation and Laplace's Theory of Probability Analysis.
The statistical significance of De Morville's work;
1 In the special case of frequency estimation probability, the accuracy of the arithmetic average of observation values is directly proportional to the square root of the observation times n, which can be regarded as a great progress in human understanding of nature.
Of course, the greatest influence of De Moivre's work on mathematical statistics lies in the central limit theorem named after him today. About 40 years after de moivre made his discovery, Laplace established a more general central limit theorem, and the most general independent and central limit theorems were finally completed in the 1930 s. Later, statisticians found that a series of important statistical data, in the sample size n->; ; ∞, and its limit distribution has a normal form, which forms the basis of this method in mathematical statistics. At present, this method plays a very important role in statistical methods. De Moifer's work can be said to be the source of this important development. Let two complex numbers (expressed in triangular form) z1= r1(cos θ1+isinθ1) and Z2=r2(cosθ2+isinθ2), then:
z 1z 2 = r 1r 2[cos(θ 1+θ2)+isin(θ 1+θ2)]。