Probability 1 at CEU -- fall semester 2018

Homework sheet 1. Solutions here.
Homework sheet 2. Solutions here.
Homework sheet 3. Solutions here.
Homework sheet 4. Solutions here.
Homework sheet 5. Solutions here.
Homework sheet 6. Solutions here.
Homework sheet 7. Solutions here.

A few midterm exercises from earlier years here.

This was the midterm exam, and here are the solutions..
This was the final exam, and here are the solutions..

No. of Credits: 3
No. of ECTS credits: 6
Time Period of the course: Fall Semester
Prerequisites: basic probability
Course Level: introductory MS
Official syllabus: here.
Classes: Tuesdays from 12:30 in room 310/A.
Course Coordinator: Imre Péter Tóth.

Schedule (planned):
week #whentopicremark
week 1-22018.09.17,24Review of basic notions of probability theory. Measure-theoretic language. Some famous problems and paradoxes.
week 32018.10.01Different types of convergence for random variables. Borel-Cantelli lemmas.
week 4-52018.10.08,15Laws of Large Numbers. The method of characteristic functions in proving weak convergence: the Central Limit Theorem.
week 6-72018.10.25,29Conditional expectation with respect to a sub-sigma-algebra. Martingales. Some martingale convergence and optional stopping theorems.Oct 22 is a holiday, the class will be moved to the 25th, 09:00.
week 8-92018.11.05,12Applications of martingales: Galton-Watson branching processes. Asymptotic results. Birth and death process. ABRACADABRA problem.
week 10-112018.11.19,26Random walks on the integers. Construction and basic properties of Brownian motion.
week 122018.12.03Probabilistic methods in combinatorics - an example.

Midterm exam:
will be on Wednesday, 31.Oct.2018 at 16:30, room 310/A

Final exam:
will be on Monday, 10.Dec.2018 at 09:00, room 310/A

Suggested literature (References):
  1. To catch up with the missing basics: W. Feller: An Introduction to Probability Theory and Its Applications, Vol. 1, 3rd Edition, Wiley, 1968.
  2. For most of the course: R. Durrett: Probability. Theory and Examples. 4th edition, Cambridge University Press, 2010.
  3. For the short combinatorics part: N. Alon, J. H. Spencer: The Probabilistic Method. 3rd edition, Wiley, 2008.

Grading rules:
There will be weekly homework assignments worth 30% of the total score. The midterm will also be worth 30%, while the final exam is worth 40%.
In detail:

Material for learning:
Some notes about the measure theoretic basics of Probability