Probability Theory II
| Title | ΘΕΩΡΙΑ ΠΙΘΑΝΟΤΗΤΩΝ ΙΙ / Probability Theory II |
| Code | 0505 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 1st / Undergraduate |
| Teaching Period | Winter |
| Common | No |
| Status | Inactive |
| Course ID | 40000523 |
Programme of Study: UPS of School of Mathematics (2014-today)
Registered students: 254
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|
| Academic Year | 2017 – 2018 |
| Class Period | Winter |
| Faculty Instructors |
|
| Weekly Hours | 3 |
| Class ID | 600099154
|
Class Schedule
| Building | Φυσικομαθηματική (Δ) |
| Floor | Όροφος 3 |
| Hall | ΑΙΘΟΥΣΑ Μ0 (199) |
| Calendar | Τετάρτη 16:00 έως 17:00 |
| Building | Φυσικομαθηματική (Δ) |
| Floor | Όροφος 3 |
| Hall | ΑΙΘΟΥΣΑ Μ0 (199) |
| Calendar | Τετάρτη 17:00 έως 19:00 |
| Building | Φυσικομαθηματική (Δ) |
| Floor | Όροφος 3 |
| Hall | ΑΙΘΟΥΣΑ Μ0 (199) |
| Calendar | Πέμπτη 12:00 έως 13:00 |
| Building | Φυσικομαθηματική (Δ) |
| Floor | Όροφος 3 |
| Hall | ΑΙΘΟΥΣΑ Μ0 (199) |
| Calendar | Πέμπτη 13:00 έως 15:00 |
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
- e-Study Guide https://qa.auth.gr/en/class/1/600099154
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
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 150 | 5 | ✓ | ||
| Reading Assigment | 20 | 0.7 | ✓ | ||
| Tutorial | 15 | 0.5 | |||
| Total | 185 | 6.2 |
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
