# Introduction to Probability (MAY331)

### General

School School of Science Department of Mathematics Undergraduate ΜΑΥ331 3 Introduction to Probability Lectures (Weekly Teaching Hours: 5, Credits: 7.5) General Background - Greek Yes (in English, reading Course) 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 entry-level 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: Exploit and apply the classical and empirical definition of probability in order to calculate probabilities, by using combinatorial analysis. Utilize the axiomatic foundation of the concept of probability and use it in order to derive and prove probabilistic laws and properties. Understand and utilize classical probabilistic laws as the multiplicative theorem, the total probability theorem, Bayes’ formula, and independence for modeling respective problems. Emphasis is given to the use of interdisciplinary problems which are modeled by the application of the above probabilistic rules. Understand the necessity of introducing and studying the concept of random variable, its characteristics (mean, variance, etc.) and the corresponding probability distribution. Special discrete and continuous distributions are defined and utilized for the description, analysis and study real problems from different areas (lifetime distributions, reliability etc.). Working independently Decision-making Production of free, creative and inductive thinking Criticism and self-criticism

### Syllabus

Basic ideas and laws of probability: Sample space and events. Classical-Statistical 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 (face-to-face)

Use of Information and Communications Technology

Use of ICT in communication with students

Teaching Methods
Lectures (13X5) 65
Working independently 100
Exercises-Homeworks 22.5
Course total 187.5
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)