STP 421 – Probability

Spring 2012

Instructor: Dr. Jay Taylor, office: PSA 447; phone: 965-2641; e-mail:
Time: Mondays and Wednesdays 3:30-4:45
Location: ECG G237
Office Hours: Tuesdays 1:00-4:00 in PSA 447; also by appointment.
Text: A First Course in Probability (8th Edition) by Sheldon Ross. Warning: The 7th and 8th editions cover the same material, but differ in the numbering of some of the exercises.

Course Description: This course will provide an introduction to the mathematics of uncertainty and randomness. Topics covered will include probability spaces, combinatorics, random variables, probability distributions, expectation, transformations of random variables, moment generating functions, the weak and strong laws of large numbers, and the central limit theorem. Although we will give some attention to the formal aspects of probability theory, our main focus will be on developing the skill and intuition required to solve problems in which chance plays an important role. Such problems come from many disciplines, including the life sciences (genetics, epidemiology, conservation biology), physics (materials science, quantum mechanics), meteorology, and economics.

Problem Sets: These will be announced in class and posted on the course web page at the following link. Solutions will also be posted on the course web page a few days after each set is collected. Note: I will not accept any problem sets after the solutions have been posted. For those who would like more practice with the material, additional problems (along with their solutions) can be found in the Self-Test Problems and Exercises that appear at the end of each chapter in Ross.

Grading and Assignments: There will be three exams (including the final exam), each worth 100 points. The problem sets will also be worth 100 points collectively. Of the 400 points possible, 360 or more points will guarantee an A, 320 or more will guarantee a B, 280 or more will guarantee a C, and 240 or more will guarantee a D.

Practice Exams: Exam 1 and solutions from Fall 2011. Exam2 and solutions from Fall 2011. Final Exam and solutions from Fall 2011.

Final Exam: 12:10 – 2:00 pm. on Wednesday 2 May 2012 in ECG G237.

Lecture notes: These are organized into a booklet and follow the order shown in the syllabus.



Sections in Ross

9 Jan

Overview; Probability Spaces


11 Jan

Properties of probabilities; Continuity


16 Jan

Martin Luther King Jr. Holiday

18 Jan

Ordered Samples; Permutations; Combinations


23 Jan

Multinomials; Combinatorial Identities


25 Jan

Symmetric Probability Spaces


30 Jan

Conditional Probability


1 Feb

Bayes' Formula; Subjective Probability

3.3, 2.7

6 Feb



8 Feb

Conditional Probabilities as Measures


13 Feb

Exam 1

15 Feb

Random variables; discrete distributions


20 Feb

Expectations and variances of discrete distributions


22 Feb

Binomial distribution


27 Feb

Poisson distribution


29 Feb

Geometric and other distributions


5 March

CDFs; Continuous RVs

4.10, 5.1

7 March

Expectation and Variance; Uniform distribution

4.9, 5.2-5.3

12 March

Normal distribution


14 March

Exponential and related distributions


19 March

Spring Break

21 March

Spring Break

26 March

Functions of RVs.


28 March

Joint distributions; Independent RVs. Exam 2 distributed.


2 April

Sums of independent RVs; Convolutions. Exam 2 collected (Solutions).


4 April

Conditional distributions


9 April

Expectations of sums


11 April

Covariance and correlation


16 April

Conditional expectation


18 April

Moment generating functions


23 April

Weak and Strong Laws of Large Numbers; Central Limit Theorem