# MAT-02506 Probability Calculus, 4 cr

#### Lisätiedot

This course will no longer be lectured. In the future, take MAT-01566 Mathematics 5 instead.
Ei toteuteta lukuvuonna 2019-2020.

Henri Hansen

#### Opetus

 Toteutuskerta Periodi Vastuuhenkilö Suoritusvaatimukset MAT-02506 2019-01 - Henri Hansen

#### Osaamistavoitteet

In this course, the students learn the basic concepts of probabilities, random variables and random vectors. The students learn to compute discrete and continuous probabilities and expectation values such as variances and correlations. The students also learn to apply the probability calculus to practical problems. The students learn how to justify their claims using mathematical methods and to present their solutions orally as well as in written form.

#### Sisältö

 Sisältö Ydinsisältö Täydentävä tietämys Erityistietämys 1. Basic Notions of Probability Theory: Probability and Expectation, Conditional Probability, Total probability and Independence Bayesian probability and Combinatorial analysis. 2. Random Variables: The Probability Mass and Density Functions, Important Discrete Random Variables, Important Continuous Random Variables and Expectation and Variance Moment Generating Function 3. Random Vectors: Discrete and Continuous Random Vectors, Covariance and Correlation, Multinormal Distribution and The Central Limit Theorem Transformations of Random Vectors

#### Ohjeita opiskelijalle osaamisen tasojen saavuttamiseksi

The grade of the course is based on the final exam and exercises.

#### Arvosteluasteikko:

Numerical evaluation scale (0-5)

#### Esitietovaatimukset

 Opintojakso P/S Selite MAT-01166 Mathematics 1 Mandatory MAT-01266 Mathematics 2 Mandatory MAT-01366 Mathematics 3 Mandatory

#### Vastaavuudet

Opintojakso ei vastaan mitään toista opintojaksoa

 Päivittäjä: Ullgren Sini, 10.04.2019