Probability 1 at CEU -- fall semester 2013

All results of the semester, including grades are here for those who requested that I publish them online. These results are preliminary at present. You can look at your corrected final exams and complain if I corrected them wrong.
See the detailed description of the grading below.

The questions of the final exam will be here when I find them, and here are the solutions.

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Sample exercises for the exam here.
These were the questions of the replacement midterm, and here are the solutions.
These were the questions of the midterm, and here are the solutions.
These were the questions of the "placement test".

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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.
Homework sheet 8. Solutions here.
Homework sheet 9. Solutions here.

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During class, some people requested that I publish a longer (than the homework sheets) list of exercises that are relevant for the midterm. So here is a very long list of exercises from the Durrett book. Don't try to look at them all, just pick a few from different chapters to get an idea.

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No. of Credits: 3
No. of ECTS credits: 6
Time Period of the course: Fall Semester
Prerequisites: basic probability
Course Level: introductory MS
Syllabus: here. Classes: Mondays from 14:30 in room 310/A.
Course Coordinator: Imre Péter Tóth.

Schedule (planned):

week #	when	topic	remark
week 1-2	2013.09.16,24	Review of basic notions of probability theory. Measure-theoretic language. Some famous problems and paradoxes.
week 3	2013.09.30	Different types of convergence for random variables.Borel-Cantelli lemmas.
week 4	2013.10.07	Laws of Large Numbers. The method of characteristic functions in proving weak convergence: the Central Limit Theorem.
week 5-6	2013.10.14,21	Conditional expectation with respect to a sub-sigma-algebra. Martingales. Some martingale convergence and optional stopping theorems.
week 7	2013.10.28	Applications of martingales: Galton-Watson branching processes. Asymptotic results. Birth and death process.
week 8-9	2013.11.04,11	Probabilistic methods in combinatorics. Second moment method, Lovász Local Lemma.
week 10	2013.11.18	Some large deviation theorems, Azuma's inequality.
week 11-12	2013.11.25,12.02	Random walks on the integers. Construction and basic properties of Brownian motion.

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.

Midterm, exam:
Midterm: 6 November 2013 (Wednesday) 10:00 !!TIME CHANGE!!
Final exam: 9 December 2013 (Monday) 14:30, room 310/A. !!TIME CHANGE!!

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

• The solution to each homework was evaluated with a "code" with the following meaning:
  • "3" means correctly solved
  • "2" means solved with some error
  • "1" means started on a correct track, but not solved
  • "0" means completely wrong.
  At the end of the semester these codes were translated to a homework score. At the translation, the big difference was between "solved" and "not solved", so a "correctly solved" was worth 1 point, a "solved with some error" was worth 0.8 points, and the rest was worth no points at all. Since there were only 29 homeworks, the sum of these was eventually multiplied by 30/29 to give the "homework score".
• The midterm was worth 30 points, and the final was worth 40 points (plus possible extras). These were added to the homework score to give the "total score".
• The total score was translated into grades using the following table:

  score range	grade
  0-49	F
  50-59	C+
  60-67	B-
  68-75	B
  76-83	B+
  84-89	A-
  90-100	A

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