### Introduction to Probability Theory

#### 2008/2009, sem. 1

Lecturer
Prof. Boris Tsirelson, School of Mathematical Sciences.
Time and place
Sunday 11-12 Schreiber 006, Wednesday 16-18 Ornstein 111.
Instructors
Roee Teper, Asaf Cohen.
Prerequisites
(Infinitesimal) calculus 1 (in parallel).
The final exam.

#### TOPICS

1. SETS AND PROBABILITIES
2. CONDITIONING AND INDEPENDENCE
3. RANDOM VARIABLES
4. EXPECTATION AND VARIANCE
5. LIMIT THEOREMS
1. Weak law of large numbers.
2. Central limit theorem.
3. Normal approximation to binomial distribution.

#### Exercises

Problems and solutions (courtesy of the instructor)

#### Some exams

##### Especially recommended
• [Si] SIEGRIST K., "Virtual Laboratories in Probability and Statistics"
http://www.math.uah.edu/stat/
Available online only. Free, high quality, interactive. Read it all, if you are ambitious enough; otherwise use links to specific topics (above, under the TOPICS header).
Probably you need the MathPlayer plug-in (if you use Internet Explorer rather than Mozilla Firefox); details and links on the [Si] site.
• [BT] BERTSEKAS D. (Dimitri), TSITSIKLIS J., "Introduction to probability" (2002).
A book; our library has 6 copies.
• [GS] GRINSTEAD C., SNELL J., "Introduction to probability"
http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/book.html
Available both as a usual book, and as a PDF file (free) plus additions (including interactive).
##### Books, in English
• ROSS S. (Sheldon), "A first course in probability" (1994/98).
• HOEL P. (Paul), PORT S., STONE C., "Introduction to probability theory" (1971).
• HODGES J. (Joseph), LEHMANN E., "Basic concepts of probability and statistics" (1964/70).
• FELLER W. (William), "An introduction to probability theory and its applications" Vol. 1 (1950/57/68).
• LIPSCHUTZ S. (Seymour), "Schaum's outline of theory and problems of finite mathematics" (1966/76).
##### Books, In Hebrew
• LEVIATAN T. (Telma), "Histabrut ve-Statistica le-Madaim".
• BECK A. (Amir), "Mavo leHistabrut" (2002).
• LEVIATAN T. (Telma), RAVIV A., "Histabrut" (second edition).
• LIBERMAN U. (Uri), "Mavo leTorat a-Histabrut" (third edition).
##### Books, in English
• ASH C. (Carol), "The probability tutorial book" (1993).
• BHATNAGAR P. (Prabhu), "Introductory lessons in modern mathematical concepts" (1971).
• DURRETT R. (Richard), "The essentials of probability" (1994).
• FELDMAN D. (Dorian), FOX M., "Probability: the mathematics of uncertainty" (1991).
• GOLDBERG S. (Samuel), "Probability: An introduction" (1960).
• KYBURG H. (Henry), "Probability theory" (1969).
• MCCORD J. (James), MORONEY R., "Introduction to probability theory" (1964).
• PITMAN J. (Jim), "Probability" (1993), Chapters 1-3.
• STOYANOV J. (Jordan), "Counterexamples in probability" (1987).
• SZEKELY G. (Gabor), "Paradoxes in probability theory and mathematical statistics" (1986).
• THORP E. (Edward), "Elementary probability" (1966).
• USPENSKY J. (James), "Introduction to mathematical probability" (1937).
##### Books, in Hebrew
• DVORETZKI A. (Arie), "Mavo leTorat a-Histabrut".