Probability Theory II

Course Information
TitleΘΕΩΡΙΑ ΠΙΘΑΝΟΤΗΤΩΝ ΙΙ / Probability Theory II
Code0505
FacultySciences
SchoolMathematics
Cycle / Level1st / Undergraduate
Teaching PeriodWinter
CommonNo
StatusActive
Course ID40000523

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

Registered students: 1
OrientationAttendance TypeSemesterYearECTS
CoreCompulsory Course535.5

Class Information
Academic Year2015 – 2016
Class PeriodWinter
Faculty Instructors
Weekly Hours3
Class ID
600004700
Type of the Course
  • Background
  • General Knowledge
  • Scientific Area
Course Category
Specific Foundation / Core
Mode of Delivery
  • Face to face
Digital Course Content
Language of Instruction
  • Greek (Instruction, Examination)
Prerequisites
Required Courses
  • 0201 Calculus I
  • 0202 Calculus II
  • 0203 Calculus III
  • 0502 Probability Theory I
General Prerequisites
calculus,set theory,measure theory
Learning Outcomes
Students will be able to manage all of the multidimensional distributions.
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.
Keywords
Multidimensional random variables, Conditional Probability, Random variable transform, Convergences, Central Limit Theorem
Educational Material Types
  • Book
Use of Information and Communication Technologies
Use of ICT
  • Use of ICT in Communication with Students
Course Organization
ActivitiesWorkloadECTSIndividualTeamworkErasmus
Lectures1505
Reading Assigment200.7
Tutorial150.5
Total1856.2
Student Assessment
Student Assessment methods
  • Oral Exams (Formative, Summative)
  • Γραπτές εξετάσεις (Formative, Summative)
Bibliography
Course Bibliography (Eudoxus)
Πιθανότητες ΙΙ. Θεωρία και Ασκήσεις των Σ.Κουνιά και Σ.Καλπαζίδου
Last Update
11-11-2015