# MATS260 Probability Theory 1 (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, 2023-2024

## Description

Basic concepts of probability:

- probability space
- independence of events
- random variables
- expectation and its basic properties
- independence of random variables

## Learning outcomes

The students are familiar with the concept of probability spaces, random variables, and independence.

They are able to describe simple stochastic phenomena within this framework and know important distributions. The notion of expected values along with the main theorems about integration is understood as extension of the Riemann integral.

The students are able to compute expected values based on discrete distributions and the Lebesgue measure on the real line.

They are able to describe simple stochastic phenomena within this framework and know important distributions. The notion of expected values along with the main theorems about integration is understood as extension of the Riemann integral.

The students are able to compute expected values based on discrete distributions and the Lebesgue measure on the real line.

The students have developed their deductive reasoning skills for example by deriving properties of a measure from its definition.

## Description of prerequisites

MATA280 Foundations of stochastics or TILA1200 Probability 1 or MATA2600 Basic course in probability.

## Study materials

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

## 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 3

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

**Study methods:**

Lectures and homework exercises.

#### Teaching

##### 1/9–3/12/2023 Lectures

##### 3/1–3/1/2023 Course exam

##### 3/22–3/22/2023 Course exam

x

### Exam (5 cr)

**Type:**

Exam

**Grading scale:**

0-5

**Language:**

English, Finnish