Introduction to Probability (MAY331)
 Ελληνική Έκδοση
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 Department of Mathematics
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General
School 
School of Science 

Academic Unit 
Department of Mathematics 
Level of Studies 
Undergraduate 
Course Code 
ΜΑΥ331 
Semester  3 
Course Title 
Introduction to Probability 
Independent Teaching Activities 
Lectures (Weekly Teaching Hours: 5, Credits: 7.5) 
Course Type 
General Background 
Prerequisite Courses   
Language of Instruction and Examinations 
Greek 
Is the Course Offered to Erasmus Students 
Yes (in English, reading Course) 
Course Website (URL)  See eCourse, the Learning Management System maintained by the University of Ioannina. 
Learning Outcomes
Learning outcomes 
The aim of this course is to provide with a comprehensive understanding of the basic definitions of probability and the basic principles and laws of probability theory. Further, the introduction to the concepts of the random variable and the distribution function, as well as, their characteristics, such as the mean, variance, moments, moment generating function, etc., is included in the main aims of the course. Special distributions, such as binomial, geometric, Pascal, Poisson, uniform, exponential, gamma, normal distribution, etc. are studied and their use and application is indicated. The course is compulsory, it is of an entrylevel and it aims to develop skills that help the students to understand, design and exploit stochastic models to describe real problems. At the end of the course the students is expected to be able to:


General Competences 

Syllabus
Basic ideas and laws of probability: Sample space and events. ClassicalStatistical and Axiomatic definition of probability. Properties of probability and probabilistic formulas and laws. Elements of combinatorial analysis. Random variables and distribution functions. Discrete and continuous random variables and distribution functions. Standard discrete and continuous distributions: Binomial, Geometric, Pescal, Poisson, Uniform, Exponential, gamma, Normal etc. Characteristics of random variables and probability distributions: Expectation, variance, moments, moment generating function, properties. Transformation of random variables.
Teaching and Learning Methods  Evaluation
Delivery 
Classroom (facetoface)  

Use of Information and Communications Technology 
Use of ICT in communication with students  
Teaching Methods 
 
Student Performance Evaluation 
Final written exam in Greek (in case of Erasmus students in English) which concentrates on the solution of problems which are motivated by the main themes of the course. 
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
 Ι. Κοντογιάννης, Σ. Τουμπής. Στοιχεία πιθανοτήτων, [Προπτυχιακό εγχειρίδιο]. Κάλλιπος, Ανοικτές Ακαδημαϊκές Εκδόσεις. https://hdl.handle.net/11419/2810.
 J. Blitzstein, J. Hwang. Introduction to Probability, 2nd edition, CRC Press, 2019.
 R. Dobrow. Probability with Applications and R, Wiley, 2014.
 H. Tijms. Understanding Probability, 3rd edition, Cambridge University Press, 2012.
 H. Tijms. ProbabilityQ a lively introduction, Cambridge University Press, 2018.
 [Περιοδικό / Journal] Annals of Probability (IMS)
 [Περιοδικό / Journal] Electronic Journal of Probability (IMS)
 [Περιοδικό / Journal] Journal of Applied Probability (Cambridge University Press)