Courses

Probability Theory and Statistics

General

Course Contents

Probability Theory as a framework for describing and analyzing uncertainty. An overview of Set Theory. Basic Probability Models and Axioms.
Independent events. Basic Listing Principle. Combinatorial Principles, Discrete Probability Calculation Applications.
Conditional Probability, Total Probability Theorem, Multiplication Rule, Bayes Theorem. Statistical Independence.
Random Variables: Definition of discrete and continuous random variables, Cumulative Distribution Function, Probability Mass Function, Probability Density Function.
Discrete Random Variables: Moments, Basic Distributions.
Continuous random variables: Moments, Basic Distributions.
Normal Random Variables: Properties, Standard Normal Distribution.
Multiple Random Variables: Joint and Marginal Distributions, Statistical Independence, Derived Distributions: Sum of Independent Random Variables.
Joint Moments.
Boundary Theorems: Markov and Chebyshev Inequalities, Laws of Large Numbers, Central Limit Theorem.
Descriptive Statistics: Frequency Tables, Barcharts, Histograms, Stemplots, Dot Diagrams, Location Measures, Variability Measures.
Statistical Inference, Parameter Estimation, Point Estimation (Moments Method, Maximum Likelihood Estimation), Confidence Intervals. Linear Regression.

Educational Goals

This course is designed as an introduction to the basic concepts of Probability Theory and Statistics, introducing the fundamentals for the analysis of probability models. Probabilistic modeling is widely used in the engineering sciences as it is a prerequisite for data processing and drawing conclusions and is fundamental to decision making. Students are invited to study the theoretical foundations of probability theory and mathematical statistics and will understand types of practical problems involving uncertainty, related to engineering as well to other scientific fields such as medicine and economics.
On completion of the course, students should be able to:
(a) manipulate the basic concepts of probabilities and calculate them in terms of the possible results of an event;
(b) understand and apply the basic methodologies for analyzing and solving uncertainty problems using models of random variables;
(c) analyze statistical data by hypothesis testing and parameter estimating and draw conclusions; and
(d) attend, without significant gaps, more specialized industrial engineering and management courses.

General Skills

Research, analysis and synthesis of data and information, using corresponding technologies, Adaptation to new situations, Decision making, Working in an international environment, Independent work, Teamwork – distribution of responsibilities, Working in an interdisciplinary environment, Practicing criticism and self-criticism, Promoting free, creative and inductive thinking.

Teaching Methods

Lectures, Exercises, Online guidance, Projected Presentations, E-mail communication, Online Synchronous and Asynchronous Teaching Platform (moodle).

Students Evaluation

Assessment Language: English / Greek
The grade of the course is formed 100% by a written final examination including problem solving, graphs, diagrams and calculations based on data.

Recommended Bibliography

Introduction to Probability, 2nd E, Dimitri P. Bertsekas and John N. Tsitsiklis, ISBN-13: 978-1886529236.
Probability and Statistics, Murray R. Spiegel (Schaum’s Outlines), ISBN-13: 978-0071350044
Probability, Random Variables, and Stochastic Processes, 4th E, Athanasios Papoulis, S. Unnikrishna Pillai, ISBN-13: 978-0071226615