# Probability Theory I

 Title ΘΕΩΡΙΑ ΠΙΘΑΝΟΤΗΤΩΝ Ι / Probability Theory I Code 0502Α Faculty Sciences School Mathematics Cycle / Level 1st / Undergraduate Teaching Period Winter Common No Status Active Course ID 600019632

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

Registered students: 413
OrientationAttendance TypeSemesterYearECTS
CoreCompulsory Course326

 Academic Year 2021 – 2022 Class Period Winter Faculty Instructors Ioannis Antoniou 39hrs Instructors from Other Categories Vasileios Karagiannis 65hrs Weekly Hours 4 Class ID 600187023
SectionInstructors
1. ΤΜΗΜΑ ΑIoannis Antoniou
2. ΤΜΗΜΑ ΒIoannis Antoniou
Course Type 2016-2020
• Background
• Scientific Area
Course Type 2011-2015
General Foundation
Mode of Delivery
• Face to face
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
• Greek (Instruction, Examination)
• English (Examination)
Prerequisites
Required Courses
• 0201 Calculus I
• 0202 Calculus II
General Prerequisites
Basic knowledge of Mathematical Analysis
Learning Outcomes
1. Acquaintance with the Probabilistic-Stochastic Thought. 2. know how to use the combinational analysis methods in solving problems of probabilities. 3. use conditional probabilities, total probability, Bayes rule, Poincare theorem, product law and apply them to probability problems. 4. know the notion of distribution function, probability function and probability density function, how to calculate them for discrete and continuous random variables and how to manipulate functions of random variables, 5. can calculate parameters of distributions (mean, variance and other moments), calculate and manipulate probability generator function and moment generator function, 6. know and use basic univariate 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
Lectures521.7