====== 3 - Review: Probabilities ======

February 16th, 2010.\\
February 18th, 2010.


=== Notes ===

Lecture notes:
   * Linear algebra: [[cos424>slides/ela.pdf|pdf]] [[cos424>slides/ela.tex|tex]]
   * Probabilities: [[cos424>slides/prob.pdf|pdf]] [[cos424>slides/prob.tex|tex]]
Scribe notes:
   * Feb 16th:  [[cos424>slides/3-notes-valentino-misener.pdf|J.Valentino & R.Misener]]
   * Feb 18th:  [[cos424>slides/3-notes-scott.pdf|W.Scott]]


=== Summary ===

Addendum:
   * How to solve a linear system, in practice.

\\

Probabilities:
   * Discrete probabilities, random variables
   * Conditional probabilities, independence
   * Application: the Monty-Hall problem.
   * Expectation and variance.
   * Law of large numbers.
   * Continuous probability distribution.
   * Probability density.
   * Normal law, strong law of large numbers.
   * Confidence intervals


=== Books ===

There are lots of competent textbooks discussing 
mathematical concepts that are useful for our course.
The following selection is by no means exhaustive.

   * B. V. Gnedenko, A. Ya. Khinchin: //An Elementary Introduction to the Theory of Probability//. W. H. Freeman and co., 1961 \\  Translation from a russian standard: this small book covers the bases with a lot of unusual examples.  

   * P. Billingsley: //Probability and Measure, 3rd Edition//. Wiley-Interscience, 1995. \\ The other end of the spectrum in probability theory. A definite reference for all kinds of sophisticated material.

   * L. N. Trefethen and D. Bau: //Numerical Linear Algebra//. SIAM, 1997. \\ A highly rated graduate textbook on numerical algorithms for linear algebra.

   * P. G. Ciarlet: //Introduction to Numerical Linear Algebra and Optimization//. Cambridge University Press, 1989. \\ This book keeps things short and precise. Do not expect to turn the pages quickly. Excellent on optimization.

=== Readings ===

   * (optional) //[[cos424>papers/FreedmanStark2003.pdf|What is the chance of an earthquake?]]// (Freedman and Stark, 2003)