# Probability Theory Fall 2024

#### Overview

Welcome to my course on Probability Theory for third-year students of Bachelor’s Programs “Computer Science” and “Biomedical Engineering” at MIPT.

This is the second part of the course. We will devote this semester to the study of convergence of random variables, limit theorems, gaussian vectors and conditional expectation.

## Problem sets

Problem set 1. [answers] Random vectors. Convolution and Expectation.

Problem set 2. [answers] Convergence of random variables.

Problem set 3. [answers] Characteristic functions.

Problem set 4. [answers] Limit theorems.

Problem set 5. [answers] Gaussian vectors.

Problem set 6. [answers] Conditional Expectation.

Problem set 7. [answers] Conditional distributions.

Problem set 8. [answers] Random Walk.

Problem set 9. [answers] Branching Process.

Problem set 10. [answers] Wiener Process.

## Attendance & Marks

#### Course guidelines and grading system

At the end of this course, you will get a grade from 0 to 10 (you need at least 3 to pass) according to the following parameters:

- A:= Max of 1 point for class attendance (1 if you missed no more than 1 class. And o,5 if you missed no more than 2)
- P:= Max of 2 points for participation in class by solving homework on the board.
- T:= Max of 6 points for Test 1 + Test 2
- E:= Max of 4 points for final exam (зачет) on theory

Final grade = A+P+T+E-2

**IMPORTANT: ***You must get at least 1.5 points in the final exam on theory in order to pass the course.*

The theoretical exam and tests 1 and 2 are ** closed-book**, that is, you are not allowed to use any material.

The number of points you get for each activity, is either an integer x or x+0.5.

If your final grade (after the final exam) is not an integer (z+0,5), you can solve an extra problem to raise your grade to z+1. Otherwise you get just z.

If you have <= 2 points for A+T, then you have a solve problems in the exam. You need a minimum number of points of the solution of these problems to get your theoretical questions and continue with the exam.

On the other hand, in the retake you have to solve problems independently from the number of points you have for T.

#### Recommended literature

(Graduate Texts in Mathematics) 2nd Edition - Albert N. Shiryaev.**Probability**- Stanley H. Shan. [download]**Introduction to probability for Data Science**- Carlos Fernandez-Granda.**Probability and Statistics for Data Science**- Joseph K. Blitzstein, Jessica Hwang.**Introduction To Probability**- Мера и интеграл, Дьяченко М.И.
- Курс теории вероятностей и математической статистики, Севастьянов Б.A.
- Курс теории вероятностей, Чистяков В.П.

#### Recommended extra material

- Short lectures on measure theory: [playlist]
- Short lectures on Probability Theory [playlist]
- Probability theory course IMPA [playlist]
- Probability theory course Harvard University [playlist]
- Interactive videos on probability from 3Blue1Brown [video]
- Lectures in introduction to probability (in russian) [playlist]
- [link]