Introduction to Probability. Math 3100, Section 2. Spring 2016

TuTh 11am-12:15 pm, Gibson 211.


Prerequisites and expectations:

The official prerequisite for this course is Math 1320 Calculus II, and it is an essential prerequisite for two reasons. First Math 1320 is required to ensure that students taking 3100 have sufficient mathematical maturity. Second, Math 3100 uses a lot of concepts and techniques from calculus. These include basic properties of exponential and logarithmic functions (technically this is precalculus material, but it is often studied in calculus), integration techniques (mostly substitution and parts), basic techniques for computing limits and basic results on convergence of series and power series. If it has been a while since you have taken calculus, you are encouraged to review this material in the first few weeks (most of it will not be needed until the second half of the course). Important: If you have never taken Math 1320 (or equivalent), you should talk to me at the beginning of the semester to ensure that you have sufficient background for 3100.

It is not expected that you have taken a proof-based course prior to 3100 and this course will not emphasize abstract proofs, but there will be some theoretical questions in both exams and homeworks.

Reading assignments: There will be a required reading assignment before each class (usually from our main textbook), and I will expect that you have at least looked over that material before the class. This should allow us to save time on the theoretical part and spend more time on examples.

Very tentative schedule.

week sections topics
Jan 21 1.2 Probabilistic models.
Jan 26, 28 1.3, 1.4 Conditional Probability. Bayes' Rule
Feb 2, 4 1.5, 1.6 Independence. Counting.
Feb 9, 11 2.1, 2.2, 2.3 Discrete Random Variable. Probability Mass Functions (PMF). Functions of Random Variables.
Feb 16, 18      2.4, 2.5 Expectation, Mean and Variance. Joint PMFs
Feb 23, 25 2.6, 2.7 Conditioning and independence for discrete random variables.
Mar 1 3.1 Continuous Random Variables and PDFs.
Mar 15, 17 3.2, 3.3 Cumulative Distribution Functions. Normal Random Variables.
Mar 22, 24 3.4, 3.5 Joint PDFs and Conditioning for Continuous Random Variables.
Mar 29, 31 4.1, 4.2, 4.3 Derived Distributions. Covariance and Correlation. Conditional Expectation and Variance Revisited.
Apr 5,7 5.1, 5.2, 5.3 Markov and Chebyshev Inequalities. The Weak Law of Large Numbers. Convergence in Probability.
Apr 12,14 5.4, 5.5 The Central Limit Theorem. The Strong Law of Large Numbers.
Apr 19, 21 6.1 The Bernoulli Process.
Apr 26, 28 6.2 The Poisson Process.
May 3 Review.


The course grade will be based on homework homework, quizzes, one midterm and the final (all in-class), with weights distributed as follows:


The midterm date given below is tentative and may be changed later. The date and time of the final exam is determined by the registrar and cannot be changed.

Homeworks and quizzes

Make-up policy

Collaboration policy on homework.


Major announcements will be made in class and also posted on the course webpage. Some other announcements may only be made by e-mail, so check your e-mail account regularly.

Add/drop/withdrawal dates:

Special statement

All students with special needs requiring accommodations should present the appropriate paperwork from the Student Disability Access Center (SDAC). It is the student's responsibility to present this paperwork in a timely fashion and follow up with the instructor about the accommodations being offered. Accommodations for test-taking (e.g., extended time) should be arranged at least 5 business days before an exam.