# TILA1300 Probability 2 (4 cr)

Study level:
Intermediate 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

Contents:

Review about random variables, generating functions, distributions of functions of random variables, laws of large numbers and the central limit theorem.

Completion mode:

Exam. The exams for foreign students are based on book S. Ross: A first course in probability (fifth edition or later).

((5th edition) Chapters 5.7, 6.7, 7.6, 8.1-8.6, 10.1-10.2)

Please contact the examiner well before the exam by email.

Evaluation:

Exam is passed when one gets at least half of the maximum points

## Learning outcomes

After passing the exam the student is able to

• apply generating functions
• derive distribution and statistics for transformations of random variables
• use inequalities and laws of large numbers and central limit theorem for estimating probabilities

## Description of prerequisites

Calculus, Probability 1

## Study materials

Lindgren, B.W. (1976): Statistical theory.

Tuominen, P: Todennäköisyyslaskenta I.

Ross, S: A first course in probability.

Schaeffer, R.L: Introduction to probability and its applications.

## Completion methods

### Method 1

Evaluation criteria:
Arviointiin vaikuttavat menestys kurssitentissä ja mahdollisesti aktiivisuus harjoitustehtävien tms. tekemisessä.
Select all marked parts

### Method 2

Description:
The exams for foreign students are based on book S. Ross: A first course in probability (fifth edition or later). Please contact the examiner well before the exam by email.
Evaluation criteria:
Exam is passed when one gets at least half of the maximum points
Select all marked parts
Parts of the completion methods
x

### Teaching (4 cr)

Type:
Participation in teaching
Grading scale:
0-5
Evaluation criteria:
Arviointiin vaikuttavat menestys kurssitentissä ja mahdollisesti aktiivisuus harjoitustehtävien tms. tekemisessä.
Language:
Finnish
Study methods:

Luennot ja harjoitukset ja kurssitentti

Study materials:

Materiaali TIMissä

No published teaching
x

### Independent Study (4 cr)

Type:
Independent study
Grading scale:
0-5
Evaluation criteria:
Exam is passed when one gets at least half of the maximum points
Language:
English, Finnish
Study methods:

Independent Study and an Exam

Study materials:

Sheldon Ross: A first course in probability (5. edition) chapters 5.7, 6.7, 7.6, 8.1-8.6, 10.1-10.2

No published teaching