# Probability Theory I

 Title ΘΕΩΡΙΑ ΠΙΘΑΝΟΤΗΤΩΝ Ι / Probability Theory I Code 0502 Faculty Sciences School Mathematics Cycle / Level 1st / Undergraduate Teaching Period Winter Common No Status Inactive Course ID 40000520

### Programme of Study: UPS of School of Mathematics (2014-today)

Registered students: 657
OrientationAttendance TypeSemesterYearECTS

 Academic Year 2018 – 2019 Class Period Winter Faculty Instructors Ioannis Antoniou 39hrs Georgios Tsaklidis 13hrs Instructors from Other Categories Vasileios Karagiannis 52hrs Weekly Hours 4 Class ID 600120795
Course Type 2016-2020
• Background
Course Type 2011-2015
General Foundation
Mode of Delivery
• Face to face
Digital Course Content
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
• Greek (Instruction, Examination)
• English (Examination)
Prerequisites
General Prerequisites
Basic knowledge of Mathematical Analysis
Learning Outcomes
Acquaintance with the Probabilistic-Stochastic Thought. Historical development of the notion of probability. Growth of skilfulness of using the combinational analysis methods and calculations and use of Combinational Analysis in the resolution of problems of probabilities. Transformation of a problem in terms of probabilities, definition of facts, calculation of simple and conditioned probabilities, application of known theorems (total probability, Bayes rule, Poincare theorem, product law). Comprehension of the notion of distribution function (d.f.) and the one of density of probability (p.d.f.) (for continuous distributions) and of probability function (p.f.) (for discrete distributions). Finding the d.f. and p.d.f. or p.f of a random variable that is defined as a function of given random variables. Finding parameters (mean value, variance and moments) of a given random variable. Calculation and use of the probability- or moment- generating functions. Introduction to the study of discrete bivariate distributions. Comprehension of the generation of the basic uni-variate discrete distributions: uniform, Bernoulli, binomial, Poisson, geometric, hypergeometric, and continuous distributions: uniform, exponential, normal, gamma, betta and trinomial bivariate distribution.
General Competences
• Apply knowledge in practice
Course Content (Syllabus)
Historical problems. Randomnes, the sample distribution space, events, Venn diagrams. Classical definition of mathematical probability, statistical regularity, axiomatic foundation of probability - Finite sample distribution spaces, combinatorics, geometric probabilities - Conditional probability, independence - Univariate random variables, distribution functions, function of a random variable, moments, moment-generating function, probability generating function, discrete bivariate distributions - Useful univariate distributions: Discrete (Bernouli, Binomial, Hypergeometric, Geometric, Negative Binomial, Poisson), Continuous (Uniform, Normal, Exponential, Gamma) - Applications.
Keywords
probability, random variables, distribution functions, moment-generating andprobability generating functions
Educational Material Types
• Notes
• Slide presentations
• Book
Use of Information and Communication Technologies
Use of ICT
• Use of ICT in Course Teaching
• Use of ICT in Communication with Students
Description
PowerPoint presentation of the theory
Course Organization
Lectures391.3
Tutorial130.4
Total521.7
Student Assessment
Student Assessment methods
• Written Exam with Extended Answer Questions (Summative)
• Written Exam with Problem Solving (Summative)
Bibliography
Course Bibliography (Eudoxus)
Βιβλίο [11058]: Θεωρία πιθανοτήτων I, Κουνιάς Στρατής, Μωϋσιάδης Πολυχρόνης Θ. Βιβλίο [45497]: Θεωρία Πιθανοτήτων και Εφαρμογές, Χαραλαμπίδης Χαράλαμπος Α.