Probability theory and mathematical statistics: a textbook

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Одеський національний університет імені І. І. Мечникова
The surrounding nature and the society in which we live, there are various events, such as the rain, there was an accident, and others. In order for an event has occurred it must be preceded by a set of conditions. In practice, we are often faced with the events, conditions, the occurrence of which are determined by many factors. Most of these factors are not known to us, or they are random, which in principle can not be taken into account. Therefore, when the same starting conditions, these events may occur, and possibly no, i.e. their appearance is random. Probability theory is just committed to studying the properties of the mass of random events that can be repeated many times when playing a particular set of conditions. The main task of the theory of probability is a quantitative assessment of random factors on the possibility of any random event, regardless of its nature, ie, to quantify the probability of its implementation. Despite the random nature of the occurrence of events during numerous mass reproduction of these events revealed some patterns that allow you to predict the behavior of random events under certain specified conditions. The study of these patterns on the basis of weight of random events involved in mathematical statistics, which is based on probability theory and the main task of which is limited according to the data (sample) to restore a certain degree of reliability characteristics inherent in the general population, i.e. the entire set of data imaginable, describing the phenomenon under study, random nature. Over the last few decades of the theory of probability and mathematical statistics "spun off" branches of science such as the theory of stochastic processes, queuing theory, information theory, econometric modeling, and others. This process continues today. One of the most important areas of application of the theory of probability and mathematical statistics is the economy. It is difficult to imagine the study and forecasting of economic phenomena without the use of econometric modeling, regression analysis, trend and smoothing models and other methods based on probability theory and mathematical statistics. Statistical patterns inherent in a centrally controlled, decentralized and even more economy. The presence of these concepts firmly established in the economy as a reserve stock, spare capacity, state reserves, financial risks, etc., testifies to this.
Ключові слова
Theory of probability, random variables, systems of random variables, limit theorems of probability theory, mathematical statistics
Бібліографічний опис
Probability theory and mathematical statistics: a textbook / A.V.Tyurin, A.Yu. Akhmerov ‒ Odessa: «Odessa I.I. N Mechnikovational University», 2020. - 138 p.