Probability Theory

Semester 2, 2005/2006

Prof. Boris Tsirelson, School of Mathematical Sciences.
Time and place
Sunday 11-12 Shenkar 104;
Wednesday 13-15 Melamed auditorium (006).
Shiri Alon.
(Infinitesimal) calculus 2; introduction to probability theory.
Grading policy
The final exam.


  1. General probability spaces.
  2. Random variables. Cumulative distribution function, density (if exists), quantiles. Examples, discrete and continuous (uniform, exponential, normal).
  3. One-dimensional transformations of distributions.
  4. Expectation of a random variable (and its function). Variance, moments, moment generating function. Special cases.
  5. Joint distributions and independence, marginal distributions, joint density.
  6. Infinite sequences of random variables. Borel-Cantelli lemma. Modes of convergence. Convergence of expectations. Strong law of large numbers, central limit theorem.
  7. Joint distributions: conditioning, correlation, and transformations. Conditional distributions, conditional expectation. Total probability formula (continuous case). Regression and correlation. Examples. Multidimensional transformations of distributions. Distribution and density of sum, product and quotient of one-dimensional random variables.


Problems and solutions (courtesy of the instructor)

Some exams

(in addition to lecture notes available on this site)
Available on the Web (only), in English, include some interactive pages
Books, in English
In Hebrew
In English
In Hebrew