3 - Review: Probabilities

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

Lecture notes:

• Linear algebra: pdf tex
• Probabilities: pdf tex

Scribe notes:

• Feb 16th: J.Valentino & R.Misener
• Feb 18th: W.Scott

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

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.

• (optional) What is the chance of an earthquake? (Freedman and Stark, 2003)