# ΜΥ02 - Probability Theory

### Information

Code : ΜΥ02

Type : Obligatory

Semester : 2

ECTS credits: 5

Course URL: https://eclass.hua.gr/courses/DIT155/

### Expected Outcomes

This course is designed to serve as a first undergraduate course in probability theory and to introduce students in the notion and logic of probability. This course hopes to provide students with a solid foundation in probability theory that can serve as a basis for the rest courses.

### Content

1. Random Experiments, Sample space, Sample events. Finite sample spaces, Classical Probability, Axiomatic foundation of Probability

2. Conditional Probability and Stochastic Independence of Events and Experiments

3. Random Variables, Distribution Function, Probability Function, Probability Density Function

4. Distribution of a Function of a Random Variable, Expected Value, Variance of a Random Variable, Moments of a Random Variable

5. Discrete and Continuous Random Variables, Some Basic Univariate Discrete Distributions

6. Applications of Discrete Distributions to Computer Science and Telematics

7. Continuous Random Variables. Some Basic Univariate Continuous Distributions

8. Applications of Continuous Distributions to Computer Science and Telematics

9. Characteristic Function, Random Vectors, Distribution of Random Vectors, Functions of Random Vectors

10. Conditional Distributions and Moments of Conditional Distributions

11. Sequences of Random Variables

12. Convergence of Distributions, Central Limit Theorem.

### Evaluation Means

### Bibliοgraphy

1. MV Koutras 2012. Introduction to Probability Theory and Applications, Stamoulis, Athens. in Greek

2. C. Charalambides 2009. Probability Theory and Applications, Symmetria, Athens. in Greek