Probability Theory II

Course Information
TitleΘΕΩΡΙΑ ΠΙΘΑΝΟΤΗΤΩΝ ΙΙ / Probability Theory II
Cycle / Level1st / Undergraduate
Teaching PeriodSpring
Course ID600019644

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

Registered students: 729
OrientationAttendance TypeSemesterYearECTS
CoreCompulsory Course426

Class Information
Academic Year2020 – 2021
Class PeriodSpring
Faculty Instructors
Weekly Hours4
Class ID
1. ΤΜΗΜΑ ΑGeorgios Afendras, Georgios Tsaklidis
2. ΤΜΗΜΑ ΒGeorgios Afendras, Georgios Tsaklidis
Course Type 2016-2020
  • Background
  • General Knowledge
  • Scientific Area
Course Type 2011-2015
Specific Foundation / Core
Mode of Delivery
  • Face to face
Digital Course Content
The course is also offered to exchange programme students.
Language of Instruction
  • Greek (Instruction, Examination)
Required Courses
  • 0201 Calculus I
General Prerequisites
calculus,set theory,measure theory
Learning Outcomes
Upon successful completion of the course students will be able to: 1. calculate the marginal random variables of a multidimensional random variable; 2. calculate the conditional random variables of a multidimensional random variable; 3. calculate moments of multidimensional random variables; 4. calculate and use the moment generator function of a multivariate random variable; 5. use/apply the Central Limit Theorem.
General Competences
  • Apply knowledge in practice
  • Adapt to new situations
  • Make decisions
  • Work autonomously
  • Work in an international context
  • Generate new research ideas
  • Appreciate diversity and multiculturality
  • Respect natural environment
  • Demonstrate social, professional and ethical commitment and sensitivity to gender issues
  • Be critical and self-critical
  • Advance free, creative and causative thinking
Course Content (Syllabus)
The algebra of events - Probability Space - The axioms of Probability - Random variables - The notion of stochastic distribution - Multidimensional random variables - Multidimensional distribution functions - Marginal distributions - Denumerable multidimensional random variables - Continuous multidimensional distributions - Multidimensional normal distribution - Stochastic independence - Conditional Probability - Conditional density - Conditional distributions - Mean values for multidimensional random variables - Conditional mean values - Regression line - Mean square error - Random variable transforms - Compound distributions - Inequalities - Multiple Correlation coefficient - Ordered random variables - Characteristic functions - The sum of independent random variables - Characteristic functions of multidimensional random variables - Moment generating functions - Probability generating functions - Limit theory of random variables - Convergences - Relations between convergences - Central Limit Theorem - Laws of large numbers - The log log law.
Multidimensional random variables, Conditional Probability, Random variable transform, Convergences, Central Limit Theorem
Educational Material Types
  • Notes
  • Video lectures
  • Interactive excersises
  • Book
Use of Information and Communication Technologies
Use of ICT
  • Use of ICT in Communication with Students
Course Organization
Reading Assigment1103.7
Student Assessment
Student Assessment methods
  • Oral Exams (Formative, Summative)
  • Γραπτές εξετάσεις (Formative, Summative)
Course Bibliography (Eudoxus)
ΠΙΘΑΝΟΤΗΤΕΣ ΙΙ Θεωρία και Ασκήσεις, Στρατή Κουνιά και Σοφίας Καλπαζίδου (ISBN set 960-431-115-8, ISBN T.II 960-431-117-4) ΘΕΩΡΙΑ ΠΙΘΑΝΟΤΗΤΩΝ ΚΑΙ ΕΦΑΡΜΟΓΕΣ, Χαράλαμπου Α. Χαραλαμπίδη (ISBN 978-960-266-265-6)
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