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# Probability Theory and Mathematical Statistics

2023/2024
Учебный год
ENG
Обучение ведется на английском языке
6
Кредиты
Статус:
Курс по выбору
Когда читается:
1-й курс, 3, 4 модуль

### Course Syllabus

#### Abstract

This course is designed as an introduction to basic concepts of Probability Theory and Statistics with the emphasis on practical problems. It’s divided into two main parts Probability Theory (Module 3) and Statistics (Module 4). Topics include -combinatorics, -conditional probability, -random variables, -limit laws, -statistical point estimation, -hypothesis testing. The main topics are also illustrated and studied in computer statistical programs such as R, Excel, Mathematica

#### Learning Objectives

• 1. Studying the theoretical foundations of probability theory and mathematical statistics, their practical development through the construction of mathematical models and solving statistical problems 2. Understanding the types of practical problems, including those arising in sociology, which can be solved using statistical methods, and the ability to use the knowledge gained to solve them 3. Ability to work with programs for mathematical calculations 4. Deepening and expanding the range of knowledge about applied mathematical methods 5. Mastering modern methods of data analysis, for example, basic skills of data research using statistical packages such as R (S-plus)

#### Expected Learning Outcomes

• constructs confidence intervals for the means and proportions and explains their meaning
• constructs mathematical model, describing a given random experiment
• applies tables of standard normal distributions to compute probabilities and quantiles
• calculates sample mean, sample variances, sample proportion, sample quantiles and is able to do this by means of computer programs
• correctly constructs the null and the alternative hypothesis
• describes a random experiment and a sample set
• performs computations of conditional probabilities

#### Course Contents

• Combinatorics and Bernoulli trials.
• Conditional probability. Bayes' formula.
• Discrete and continuous random variables.
• Normal distribution and Central Limit Theorem
• Statistical Point estimation.
• Interval estimation.
• Hypothesis testing.

#### Assessment Elements

• Mini-tests
Mini-tests (30-minutes) ∑ Критерии оценивания «Excellent» (9-10) Has correct brilliant solutions of all tasks. Applies non-standard ways of solutions and can explain them clearly; «Excellent» (8) Has a clear argument and correct solutions. Fully satisfies all the requirements of the task; rare minor arithmetical errors occur; «Good» (6-7) Clear, explicit argument and solutions. Covers the requirements of the task; may produce occasional errors. «Satisfactory» (4-5) May make frequent errors. «Fail» (0-3) Fails to demonstrate any appropriate knowledge. Комментарий This mark is constructed as an average of Mini-tests. The duration of each mini-test is 30 minutes. Mini-tests are given more frequently than usual tests. They are used for more regular control of students knowledge and understanding. The rounding to the nearest integer is used.
• Test 1
All students must write the Tests and Mini-tests at the time that the teacher announced in advance. Those, who are absent at the Tests by legitimate reasons (medical reasons confirmed by the corresponding medical documents), will have an opportunity to write the test at the end the course. If a student was absent at the tests without legitimate reasons he/she gets 0 for this test. In case of online test, all students must keep Otherwise, the professor has a right to put 0. It is forbidden to use the internet resources, internet calculators, and social networks for this test. It is forbidden to communicate with anybody during this test. Otherwise, the professor has a right to put 0. The results and personal mistakes are discussed at the consultations with the teacher.
• Test 2
All students must write the Tests and Mini-tests at the time that the teacher announced in advance. Those, who are absent at the Tests by legitimate reasons (medical reasons confirmed by the corresponding medical documents), will have an opportunity to write the test at the end the course. If a student was absent at the tests without legitimate reasons he/she gets 0 for this test. Otherwise, the professor has a right to put 0. It is forbidden to use the internet resources, internet calculators, and social networks for this test. It is forbidden to communicate with anybody during this test. Otherwise, the professor has a right to put 0. The results and personal mistakes are discussed at the consultations with the teacher.
The activity grade includes regular home work solution and its demonstration, questions during and after lectures. Also there will be quizzes by using kahoot.com or mentimeter.com. The best students in quizzes will get additional points for the activity grade.
• Self-study
The goal of this task is independent work with mathematical literature, extraction the main ideas from a given mathematical book chapter. After the work with the given literature, the student should present the material to the teacher (or a teacher assistant) keeping the structure: introduction, the main results, conclusion. The part "main results" should contain the most important formulas, ideas, theorems clearly explained. The teacher (teacher assistant) has a right to ask additional questions or/and give additional tasks connected with the subject of the given material.
• Exam
At the exam, it is forbidden to use any notes and any copybooks, as well as any gadget with internet. The students who violate these rules will get a warning, if they violate the rules twice they will get 0.

#### Interim Assessment

• 2023/2024 4th module
0.11 * Activity gradе + 0.25 * Exam + 0.18 * Mini-tests + 0.1 * Self-study + 0.18 * Test 1 + 0.18 * Test 2

#### Recommended Core Bibliography

• A first course in probability, Ross, S., 2010
• Essentials of statistics for the behavioral sciences, Gravetter, F. J., 2014