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Syllabus

General Description

This is an introductory course to probability theory and its applications. Some of the topics that will be covered include: combinatorial analysis, axioms of probability and independence, conditional probability, Bayes' theorem, random variables (discrete and continuous), joint probability distributions, properties of expectation, the central limit theorem, the law of large numbers, and Markov chains.

Objectives

The course aims to provide an introduction to the basic ideas of probability, distribution theory and their applications. The main goal is to develop basic mathematical tools to consider models that incorporate uncertainty using a probabilistic framework.

Prerequisite(s)

Economics 11B or Mathematics 11B or 19B.

Textbook

Required: M.H. DeGroot and M.J. Schervish (2002) Probability and Statistics. Fourth Edition. Addison Wesley.

Additional References: 

  • Principles of Uncertainty. J. Kadane. Chapman & Hall. This book is available online at the UCSC Library. 
  • A First Course in Probability (sixth edition). S. Ross. Prentice Hall

Grading

There will be one midterm (35%), homework assigments (25%) and a final exam (40%). A collection of homework problems will be assigned every week but only a subset of those problems will have to be turned in and will be graded. The instructor will let you know which problems you will need to turn in as part of your graded homework assignments (homework deadlines will also be announced in class and online at least one week in advance). The exams and will be based on the weekly assigned problems. 

Homework Assignments

There will be several problems assigned every week. As mentioned above, not all the problems will have to be turned in. Only a small subset of the problems will be part of the graded homework assignments.  The assigned problems (all of them, not only the subset of graded problems) will give you a very close indication of the material that will be covered in the exams.

Reading Material

Please keep in mind that the material in this course is cumulative. You really need to stay up to date by reading the relevant book chapters and by solving related homework problems. The reading material for course will be posted online.