Бакалавриат
2025/2026
Теория вероятностей
Статус:
Курс обязательный (Прикладной анализ данных)
Где читается:
Факультет компьютерных наук
Когда читается:
2-й курс, 1, 2 модуль
Онлайн-часы:
10
Охват аудитории:
для своего кампуса
Язык:
английский
Контактные часы:
70
Course Syllabus
Abstract
"Probability Theory" is a basic academic discipline, related to the mathematical and natural science cycle of disciplines. Within the course, students will get acquainted with the theoretical foundations of modern probability theory, its main results, and learn to solve standard problems in this area. The course is of a mathematical nature, students will be able to get acquainted with the proofs of most mathematical statements. The main provisions of the discipline can be used in the future when studying the following disciplines, for example: Mathematical statistics; Machine learning; Information theory; Statistical methods for market reseach.
Learning Objectives
- To provide students with a rigorous foundation in probability theory, framing it not as an abstract mathematical exercise, but as the essential language and toolkit for modeling uncertainty, making data-driven predictions, and forming the logical basis for statistical inference in data science and business analytics.
Expected Learning Outcomes
- Define and explain the core axioms of probability, combinatorial principles, and the concepts of conditional probability and independence.
- Characterize random variables (both discrete and continuous) using Probability Mass Functions (PMFs), Probability Density Functions (PDFs), and Cumulative Distribution Functions (CDFs), and compute their expectations and variances.
- Identify and apply common probability distributions (e.g., Binomial, Poisson, Uniform, Exponential, Normal) to model real-world business and data science problems.
- Model complex scenarios involving multiple random variables using joint, marginal, and conditional distributions.
- Understand the fundamental principles of statistical inference: how sample statistics (like the sample mean) behave and distribute themselves (sampling distributions), and how this leads to point estimation and confidence intervals.
Course Contents
- Axiomatic Foundations of Probability
- Discrete Random Variables & Conditional Probability
- Parametric Families of Discrete Distributions
- Continuous Random Variables
- The Normal Distribution
- Multivariate Distributions
- Sampling Distributions
- Theory of Point Estimation
- Confidence Interval Estimation
- The Law of Large Numbers (LLN) and the Central Limit Theorem (CLT)
- Extension to Two Populations
Assessment Elements
- Homework module 1
- AttendanceRegular attendance and active participation in lectures and classes are critical for success in this course. The concepts build cumulatively, and classroom interaction is a vital component of the learning process. To encourage this engagement, class attendance will be tracked at all scheduled sessions. A mandatory oral examination triggered by low attendance is a standard assessment procedure. However, if during this examination profound discrepancies between the written work and the student's understanding are discovered then an examination score is decreased.
- Exam
- Fall Midterm
- Homework module 2
Interim Assessment
- 2025/2026 2nd module0.4 * Exam + 0.25 * Fall Midterm + 0.15 * Homework module 1 + 0.2 * Homework module 2
