# Probability Theory II

 Title ΘΕΩΡΙΑ ΠΙΘΑΝΟΤΗΤΩΝ ΙΙ / Probability Theory II Code 0505Α Faculty Sciences School Mathematics Cycle / Level 1st / Undergraduate Teaching Period Spring Common No Status Active Course ID 600019644

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

Registered students: 527
OrientationAttendance TypeSemesterYearECTS
CoreCompulsory Course426

 Academic Year 2021 – 2022 Class Period Spring Faculty Instructors Georgios Afendras 52hrs Georgios Tsaklidis 52hrs Weekly Hours 4 Class ID 600187129
SectionInstructors
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
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
• Greek (Instruction, Examination)
Prerequisites
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
• 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.
Keywords
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
Lectures521.7