# TILA2700 Further probability (5 cr)

**Study level:**

Intermediate studies

**Grading scale:**

0-5

**Language:**

Finnish

**Responsible organisation:**

Department of Mathematics and Statistics

**Curriculum periods:**

2024-2025, 2025-2026, 2026-2027, 2027-2028

## Description

The course builds on top of MATA2600 Basic course in probability, by introducing new concepts and tools. The main emphasis in the course is on continuous random numbers and random vectors. We discuss, for instance the following:

- continuous random numbers and random vectors
- probability density function, joint density, conditional density
- covariance and correlation matrices
- transformation of random variables
- law of large numbers and central limit theorem

## Learning outcomes

Student who completes the course successfully:

- can form the cumulative distribution function from a probability density function and vice versa
- can determine the expected value of a random number from its density function
- can form a joint probability density from a given marginal density and conditional density, and vice versa: can determine a marginal density and a conditional density from a given joint density
- can derive the probability density function of a transformed random number
- can determine the mean vector and covariance matrix of a linearly transformed random vector
- can apply the law of large numbers and the central limit theorem

## Description of prerequisites

Either MATA2600 Basic course in probability or TILA1200 Probability 1, and familiarity with basic integration as in MATP213 Calculus 3.

## Study materials

Lecture notes

## Completion methods

### Method 1

**Evaluation criteria:**

Menestys kurssitentissä ja mahdollisesti aktiivisuus harjoitustehtävien tekemisessä. Tarkemmat arviointiperusteet opetusohjelmassa.

Select all marked parts

### Method 2

**Evaluation criteria:**

Lopputentin pisteet.

Select all marked parts

**Parts of the completion methods**

x

### Participation in teaching (5 cr)

**Type:**

Participation in teaching

**Grading scale:**

0-5

**Language:**

Finnish

#### Teaching

##### 9/3–10/27/2024 Lectures

##### 10/30–10/30/2024 Exam

##### 11/13–11/13/2024 Exam

x

### Exam (5 cr)

**Type:**

Exam

**Grading scale:**

0-5

**Language:**

Finnish