# MATS262 Probability Theory 2 (5 cr)

**Study level:**

Advanced studies

**Grading scale:**

0-5

**Language:**

English, Finnish

**Responsible organisation:**

Department of Mathematics and Statistics

**Curriculum periods:**

2020-2021, 2021-2022, 2022-2023

## Description

- Types of convergence of random variables and measures
- Sums of independent random variables
- Convolution of probability measures
- Law of large numbers
- Central limit theorem

## Learning outcomes

After the course the student

- knows the types of convergence of random variables and measures as well as their relations to each other,
- is familiar with the behavior of sums of independent random variables, and knows the Law of large numbers and the Central limit theorem
- can identify (multidimensional) Gaussian distributions and describe their properties using characteristic functions

## Description of prerequisites

MATS260 Probability theory 1

## Study materials

Lecture notes: C. Geiss and S. Geiss: An Introduction to Probability Theory.

## Completion methods

### Method 1

**Evaluation criteria:**

The grade of the course is determined by the points aquired in the exam and in the exercises.

**Time of teaching:**

Period 4

Select all marked parts

### Method 2

**Evaluation criteria:**

The grade of the course is determined by the points aquired in the exam.

Select all marked parts

**Parts of the completion methods**

x

### Teaching (5 cr)

**Type:**

Participation in teaching

**Grading scale:**

0-5

**Language:**

English

#### Teaching

##### 3/21–5/29/2022 Lectures

##### 5/18–5/18/2022 Exam

##### 5/25–5/25/2022 Exam

x

### Exam (5 cr)

**Type:**

Exam

**Grading scale:**

0-5

**Language:**

English, Finnish