MAS203 Probability Theory, 2nd course

Department of Mathematical Statistics
Lund University with Lund Institute of Technology 

Credits
7.5 ECTS credits (5 points)


 

Lecturer
Tatyana Turova


e-mail: tatyana@maths.lth.se
office: MH:208P
Tel no: (046) 222 8543
 

Course material:
The course closely follows the book
          A. Gut, An Intermediate Course in Probability Theory, Springer 1995.
                                                        COURSE CONTENT
1. The transformation theorem.
2. Conditional density function. Conditional expectation. Conditional variance.
3. The moment generating function, the characteristic function: definitions, properties. Uniqueness theorem.
4.  Sums of a random number of random variables: expected value, variance, moment generating function.
5. Branching process: definition, moment generating function (iteration formula),
expected value, variance, probability of ultimate extinction.
6. Order statistics: joint distribution.
7. Multivariate normal distribution: characteristic function, density.
8. Multivariate normal distribution: conditional distribution.
9. Multivariate normal distribution: independence, Daly's theorem.
10. Multivariate normal distribution: quadratic forms.
11. Four types of convergence for the random variables. Theorems of uniqueness of the limits.
12.  Relations between different types of convergence.
13. Borel-Cantelli lemma.
14. The Weak Law of Large Numbers.
15. The Central Limit Theorem.
16. Convergence of the sums of the sequences of random variables.
17. The Poisson process: two definitions and their equivalence.
18. The Poisson process: superposition and thinning.
19. The distribution of the consecutive moments of occurences of the Poisson process.


 

Schedule starting 21.01: Lectures on
            Tuesday, Wednesday and  Friday 10-12 in MH:227
CURRENT  INFORMATION:
                      NO LECTURES ON MARCH 1 and 2,
BUT EXTRA LECTURES on MARCH 3,   at 10:15
                                        and on MARCH 10,  at 10:15
First meeting: Thursday January 20, MH:227 at 10:15.
Old Home work: Problems from  Chapter I: any two out of Problems 1-10.
                               Problems from Chapter II: 1-5, 11, 20-27.
                                     Problems from  Chapter III: 1,4,6,10,11, 12, 14, 15, 16, 18, 20, 23
                               Problems from  Chapter IV: 1-4, 7, 8, 9, 10, 12, 19
                                     Problems from  Chapter V: 1-3,5, 7, 11- 12, 18
       New Home work: Read A.Gut book pp.1-200.
                                        Problems from  Chapter VI:1, 2, 3, 5, 6, 7, 9, 19
                                  Problems from  Chapter VII: 1-3, 15, 16, 18

EXAMS

WRITTEN EXAM: 2005-03-14 time: 8-13 place: MH227
ORAL EXAM: 2005-03-17  time: 10-15 place: MH227
REMAKE WRITTEN EXAM: 2005-04-04  time: 8-13 place: MH227
ORAL EXAM: 2005---------    time: ------ place: MH227

OLD EXAMS

LECTURE NOTES taken previously during this course can be found at
link