ΜΥ02 - Probability Theory

General Information

School: Digital Technology

Department: Informatics and Telematics

Level: Undergraduate

Course Title: Probability Theory

Course id: ΜΥ02

Type: Background Course 

Semester: 2

Teaching and Examination Language: Greek

Is the course offered in Erasmus: Yes

Course web-page: https://eclass.hua.gr/courses/DIT155/

Activities

Lectures (Theory): 3,0

Lab lectures: 0,0

ECTS credits: 5,0

Learning 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.

General Skills

Search, analysis and synthesis of data and information
Adaptation in new conditions
Decision Making
Independent work
Work at an interdisciplinary framework
Formulation of new research ideas
Promoting reasoning and self  improvement
Promoting free, creative and deductive reasoning

Course 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.

Learning and Teaching Methods - Evaluation

Teaching methods: face-to-face

Use of ICT: 

Support the learning process through the electronic platform e-class

Course Organization

Assessment

The evaluation of each student will be made with writing exams and/or interim written exams.

Literature

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)