# MAT-01566 Mathematics 5, 5 cr

Henri Hansen

#### Opetus

 Toteutuskerta Periodi Vastuuhenkilö Suoritusvaatimukset MAT-01566 2019-01 4 Henri Hansen Final Exam and weekly exercises

#### 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 Transformations of Random Vectors 4. Sampling distributions and statistical inference: Statistics and sampling distribution, The Central Limit Theorem, prediction intervals, test of statistical hypotheses

#### Ohjeita opiskelijalle osaamisen tasojen saavuttamiseksi

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

#### Arvosteluasteikko:

Numerical evaluation scale (0-5)

#### Osasuoritukset:

Completion parts must belong to the same implementation

#### Esitietovaatimukset

 Opintojakso P/S Selite MAT-01366 Mathematics 3 Mandatory

#### Vastaavuudet

 Opintojakso Vastaa opintojaksoa Selite MAT-01566 Mathematics 5, 5 cr MAT-01560 Mathematics 5, 5 cr

 Päivittäjä: Kunnari Jaana, 05.03.2019