General Information

This course consists of an introduction to probability theory and its applications. The main goal is to develop the basic mathematical tools to consider models that incorporate uncertainty using a probabilistic framework. We start by introducing the axioms of probability and the rules needed to perform calculations with probabilities. We then move into the concepts of independence, conditional probability and Bayes theory, define a random variable, both discrete and continuous, and consider its probability distribution function as well as its expectation and higher order moments. We extend these ideas to the multivariate case. Finally we consider some more advanced topics like the Law of Large Numbers, Central Limit theorem and, time permitting, a brief introduction to some simple stochastic processes like Markov Chains and Poisson Processes.

It is assumed that students have a good working knowledge calculus. In particular, it is very important to be compotent in integration, including change of variables, and integration by parts. The class will require some multivariate integration.

  • Textbook: (required)
    • M.H. DeGroot and M.J. Schervish (2002) Probability and Statistics. Fourth Edition (if you have the third edition that's fine too). Addison Wesley.

    •  Additional Reference:  A First Course in Probability (sixth edition). S. Ross. Prentice Hall

  • Grading: There will be one midterm (35%), three quizzes but only best two scores will be used in the grade calculation (30%), and a final exam (35%). Exams and quizzes will be based on the homeworks. The quizzes will be held in class. There will be no make-up for quizzes, no exceptions, your lowest score will be dropped to allow for any event (i.e., health problems, appointments with the doctor, etc) that might prevent you from taking a particular quiz. The dates of the quizzes will be available online. In the unlikely event that a quiz date needs to be change, the new date will be announced at least one week in advance. 
  • Quiz 1: 10/11 8:55 - 9:35; Quiz 2: 11/15 8:55 - 9:35; Quiz 3: 12/01 8:50 - 9:35. Midterm: 10/27 8:00 - 9:35  Final: 12/05 9:00 - 11:00. Notice that this is a two hour final.

  • Quizzes are 40 minutes. You can have a one page, one side cheat sheet. No notes, no books. No solutions to homework problems in the cheat sheet.
  • Quizzes will be returned during sections.
  • Homework: There will be several (possibly weekly) homework assignments which will not be graded. Homeworks will give you a very close indication of the material that will be covered in exams and quizzes. Some homework will be reviewed in the sections.

  • Sections: Attendance to the sections is strongly encouraged.
    • Sisi Song: We 5:20 - 6:25, PhysSciences 140; We 6:40-7:45PhysSciences 140
    • Xingchen Yu: Mo 9:20 - 10:25, PhysSciences 140; Tu 1:30 - 2:35 PhysSciences 140
  • Grades: To get your grades for the quizzes and tests login into e-commons