Mathematical Statistics

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Theory of Probability and Mathematical Statistics

· Most of the mathematical ideas about the world and experiments are deterministic and semi- deterministic.character. In this case, when the experiment is carried out under practically the same conditions, its outcome can be accurately predicted. However, nature is more stochastic, when with each repetition of an experiment under the same conditions, it can give different, but quite definite results. Such an experiment experience (test, system, observation, process) is called random or stochastic. The outcome of a random experiment is impossible to predict. The ever-growing interest over the past decade in the theory of probability, mathematical statistics, the theory of random processes and the application of probabilistic and statistical methods in a wide variety of fields of science, technology, production and economics is explained by two reasons.

Increasing the sensitivity of modern measuring, receiving and controlling devices. As a result, random deviations of the quantitative characteristics of such devices from their average values ??play an increasingly significant role.
The development of modern means of microprocessor technology, when there was a real possibility of storing, searching and processing large arrays of probabilistic and statistical information about real objects.

When laying out the foundations of probabilistic-statistical methods, first of all, it is necessary to formulate the main subject of probabilistic modeling, probability theory, mathematical statistics and the theory of random processes. The listed mathematical disciplines, firstly, offer methods for constructing adequate models of real statistically stable experiments, and secondly, they study these models by means of mathematics and thereby discover new fundamental laws of the real world. Probability theory and mathematical statistics should be classified among the main general education disciplines that determine the modern professional level of university graduates in various specialties.

To build this course, the results and techniques of abstract probability theory, measure theory and functional analysis are used minimally and, if necessary. Along with the forced mathematical rigor, the program of the first part of the two-semester course provides for the solution of a significant number of applied problems for the direct construction and detailed study of probabilistic models that awaken and develop the intuition of a probabilistic and statistical worldview on the world. This is especially relevant in our time, when effective planning of the activities of state-owned enterprises, forecasting the situations of private companies in the financial and commodity markets, conducting election campaigns in a highly competitive environment requires probabilistic and statistical analysis of data, reliable and substantiated conclusions and forecasts. The course "Probability Theory and Mathematical Statistics" focuses on: 1) the problem of studying the approximation of qualitative and quantitative signs of statistically stable experiments; 2) the issue of mathematical formalization of the relationship between probability theory and mathematical statistics; 3) methods for constructing and analyzing adequate stochastic models of real processes and phenomena under conditions of uncertainty.

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The objectives of mastering the discipline are :

identification and study of the limiting properties of statistically stable regularities, which obey real mass phenomena;
approximation of indicators of outcomes of statistically stable experiments;
Construction and investigation of probabilistic-statis - cal models of random experiments, for which not all the conditions of their implementation are known;
an exposition of the traditional methods of presentation and preliminary analysis of statistical data related to mass phenomena in order to determine some characteristics that summarize these data;
acquaintance with methods of estimation of unknown parameters for the distribution laws of random variables and restoration of distribution laws;
acquisition of skills and ability to simulate the simplest situations of a stochastic nature using computer technology
study of the foundations of the theory of random processes.

To study the material of the course "Theory of Probability and Mathematical Statistics", knowledge of mathematics is required in the volume of the university program. In addition, to master the course of probability theory and mathematical statistics, you should especially present all sections of the courses "Probability models", "Theory of probability" and master the following important sections of mathematics:

a) elements of functional analysis, integration theory and measure theory;

b) the basics of set theory;

c) the basics of numerical methods;

d) skills in mathematical modeling and programming;

e) elements of computer technology for the use of statistical packages.

All of these are, in fact, difficult sections. Not every student will be able to master them easily. Therefore, if you need help in understanding the sections of statistics, contact the professionals https://essayassistant.org/statistics-help/ for help.

Mastering this discipline is necessary to study the following courses: "Controlled random service processes", "Statistics of random processes", "Probabilistic models in financial mathematics", "Modern problems of applied probability theory", "Modern problems of applied statistics", "Additional chapters of the theory of probability and Mathematical Statistics "," Robust Control ".

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