Бакалавриат
2018/2019
Теория вероятностей и математическая статистика
Статус:
Курс обязательный (Международный бизнес и менеджмент)
Направление:
38.03.02. Менеджмент
Кто читает:
Департамент математики
Где читается:
Санкт-Петербургская школа экономики и менеджмента
Когда читается:
1-й курс, 3, 4 модуль
Формат изучения:
без онлайн-курса
Преподаватели:
Кумачева Сурия Шакировна,
Литвинова Виктория Викторовна,
Никитин Яков Юрьевич,
Панкратова Ярославна Борисовна,
Подкопаев Олег Борисович,
Разгуляева Людмила Николаевна
Язык:
английский
Кредиты:
6
Контактные часы:
90
Course Syllabus
Abstract
Probability and Statistics has become an indispensable tool in almost every field of applied science, including social sciences. The goal of this course is to introduce the students to the basic mathematical notions, ideas and techniques needed to solve simple problems of Probability and to perform the statistical Data Analysis. The first module introduces the basic ideas and initial knowledge in Probability theory. The second module deals with the theory of random variables and Descriptive Statistics. In the third module the students will learn the basic notions of Mathematical Statistics.
Learning Objectives
- to introduce the students to the basic mathematical notions, ideas and techniques needed to solve simple problems of Probability and to perform the statistical Data Analysis
Expected Learning Outcomes
- Is able to determine the events in question, solve problems of finding the probabilities of events
- Can solve problems with sequences of Bernoulli trials
- Is able to solve problems with random variables and their characteristics
- Is able to calculate the numerical characteristics of a random variable, knows its basic properties.
- Knows the basic laws of distribution of continuous and discrete random variables
- Is able to solve the problem of constructing confidence intervals for the parameters of the normal law; hypothesis testing of the average for normal samples.
- Can use point estimation and interval estimation
- Can test parametric and nonparametric hypotheses
- can conduct correlation and regression analysis
Course Contents
- Random events and Probability axiomsRandom events. Axioms of probability, classical definition of probability, conditional probability, independent events, the law of total probability, Bayes’ rule
- Bernoulli trialsSequences of Bernoulli trials
- Random variables and their descriptionDiscreet random variables. Distribution functions of discreet random variables. Examples. Continuous random variables. Cumulative distribution function, probability density function. Examples
- Numerical characteristics of random variablesExpected value of a random variable, variance of a random variable
- Basic Laws of ProbabilityThe Law of Large Numbers, Central Limit Theorem
- Statistical sample and its descriptionDescriptive statistics. Random samples and their main characteristics. Random samples from normal distribution
- Estimation theory: basic factsPoint estimation and interval estimation
- Statistical hypothesis testingTesting of statistical hypothesis, chi-squared test
- Correlation and regressionBasics of regression analysis, least squares method, basics of correlation analysis
Interim Assessment
- Interim assessment (4 module)0.18 * Activity + 0.55 * Exam + 0.112 * Test 1 + 0.158 * Test 2
Bibliography
Recommended Core Bibliography
- Deep, R. (2006). Probability and Statistics : With Integrated Software Routines. Amsterdam: Academic Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=196153
- Young, G. A., & Smith, R. L. (2005). Essentials of Statistical Inference. Cambridge: Cambridge University Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=138968
Recommended Additional Bibliography
- Bruce, P. C. (2014). Introductory Statistics and Analytics : A Resampling Perspective. Hoboken, New Jersey: Wiley. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=923330