Math 671 — Probability Theory

Fall 2002

Instructor: Richard Durrett

Time: TR 1:25–2:40

Room: Malott 406

Text: Probability Theory and Examples, 2nd Edition.

My plan is to cover the non-starred sections in Chapters 1–3. The course assumes you have had measure theory but will begin by giving new names to familiar concepts in that subject (integral = expected value, measurable function = random variable) and introducing some concepts peculiar to probability theory (independence, Borel-Cantelli lemmas). The first main results are the weak and strong laws of large numbers, which prove that averages of a sequence of independent and identically distributed observations converges to its mean. Next comes the central limit theorem, which is the fundamental theorem of statistics, and the Poisson convergence theorem which explains the distribution of the number of people killed by horse kicks in the Prussian war or the number of points Bobby Hull scored in a hockey game. Finally, as time permits we will study random walks and prove the famous result: a drunk man will eventually find his home but a drunk bird may get lost forever.

Last modified: April 7, 2003