MATH/STAT 395 - Probability II (Summer 2006)


  • Here is the write up of the extra problems from the last lecture.
  • Typo: Practice problems, week 3, lecture 2, question 1 should be Textbook Problem 9 (not 8), from Chapter 8
  • Here is the first page of your final exam.
  • Jason is also organizing extra study hours, Thursday, 3-7pm, in Odegaard 331.
  • There will be extra office hours, Thursday, August 17th, 9-11am in Padelford C301.
  • Here is the write up explaining extra problems, as promised.
  • I'm trying out Epost - haven't used it before, so we'll see how it goes. I've created a message board called simply "395", where you guys can set up study groups, etc... it's located here. Instructions on use can be found here.

    Probability is an incredible branch of mathematics, which allows us to model and gain understanding of the random phenomena we see in the world. In this course, we continue with the foundations of probability from MATH/STAT 394. We will cover more about random variables - their joint behaviour (independent, dependent and conditional) and more ways to talk about their limits (Law of Large Numbers, Central Limit Theorem). Time permitting, we will also look at the Poisson process.

    The official prerequisite of this course is a 2.0 in MATH/STAT 394. For those of you that didn't just finish 394 - you should be familiar with the first 5 chapters of our textbook. Also, you will need to know multivariate calculus.

    Instructor: Hanna Jankowski

    I have a request: when e-mailing me, please send plain text files and try to stay away from html - it's very difficult for me to read. Thanks in advance.

    Office Hours: In my office, Padelford B220, after each lecture until noon (beginning July 24th). I will not have office hours after the test. However, I will most likely have additional office hours beforehand - these will be announced.

    If you cannot make it to my office hours, please schedule an appointment.

    Lectures will be held in BLM 309.

    The text for this course is A First Course in Probability Theory, by Sheldon Ross, 7th Edition.

    There is a copy of both the 7th and 6th edition of this text available for short-term loan from the Mathematics Research Library in Padelford Hall C-306. I have also requested that the text by John A. Rice, Mathematical Statistics and Data Analysis be placed on reserve there. It's a more advanced text, but I like the explanations.

    Grading Scheme

    There will be two assignments, a term test and a final in this course. The tentative schedule and (not so tentative) weighting scheme is as follows:

    Assignment 1 : due Monday, July 31st, 10%

    Assignment 2 : due Monday, August 14th, 10%

    Note: all assignments are due at the beginning of each lecture. There are no exceptions. I do not accept late assignments.

    Term test: Friday, August 4th, 35%

    Final: Friday, August 18th, 45%

    Note: all tests/final will be held during regular lecture times. They will be held in SMI205.

    Bonus Presentations:
    You will have the opportunity to earn bonus marks (up to a maximum of 5%) by presenting a problem, chosen by me, to the class. Interested students should let me know asap.

    Course Policies etc.

    Material Covered and Practice Problems:

    In this section I will keep an ongoing list of the material we have covered, and the suggested practice questions attached to each lecture. It is imperative that you work through these on a timely basis.

    We have covered the following sections/topics:

    Week 0 :

  • Introduction and review

    Week 1:

  • Transformation of univariate distributions (5.7)
  • Joint distributions and marginals (roughly 6.1)
  • Conditional distributions, independence, and distributions of sums of rvs (6.2, 6.3, 6.4, 6.5)

    Week 2:

  • Distribution of quotients, bivariate transformations (6.7); covariance; expectations for functions of several rvs; properties(7.1, 7.4)
  • More practice with material from Monday's lecture, general review
  • Midterm!!

    Week 3:

  • Conditional Expectation (7.5, 7.6) and moment generating functions (7.7)
  • Convergence in Probability, Chebychev's inequality (please note, we did a different version than the one in the book) , Weak Law of Large Numbers (8.1-8.3)
  • CLT (8.4)

    Week 4:

  • Poisson Process (9.1), Order Statistics (6.6)

    Practice (non-credit - do not hand these in) problems:

    Week 1
    Week 2
    Week 3
    Week 4