STP 421 – Probability

Spring 2012

Instructor: Dr. Jay Taylor, office: PSA 447; phone: 965-2641; e-mail: jtaylor@math.asu.edu
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.


Date

Topic

Sections in Ross

9 Jan

Overview; Probability Spaces

2.1-2.4

11 Jan

Properties of probabilities; Continuity

2.6

16 Jan

Martin Luther King Jr. Holiday


18 Jan

Ordered Samples; Permutations; Combinations

1.1-1.4

23 Jan

Multinomials; Combinatorial Identities

1.5

25 Jan

Symmetric Probability Spaces

2.5

30 Jan

Conditional Probability

3.1-3.2

1 Feb

Bayes' Formula; Subjective Probability

3.3, 2.7

6 Feb

Independence

3.4

8 Feb

Conditional Probabilities as Measures

3.5

13 Feb

Exam 1


15 Feb

Random variables; discrete distributions

4.1-4.2

20 Feb

Expectations and variances of discrete distributions

4.3-4.5

22 Feb

Binomial distribution

4.6

27 Feb

Poisson distribution

4.7

29 Feb

Geometric and other distributions

4.8

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

5.4

14 March

Exponential and related distributions

5.5-5.6

19 March

Spring Break


21 March

Spring Break


26 March

Functions of RVs.

5.7

28 March

Joint distributions; Independent RVs. Exam 2 distributed.

6.1-6.2

2 April

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

6.3

4 April

Conditional distributions

6.4-6.5

9 April

Expectations of sums

7.1-7.2

11 April

Covariance and correlation

7.4

16 April

Conditional expectation

7.5

18 April

Moment generating functions

7.7

23 April

Weak and Strong Laws of Large Numbers; Central Limit Theorem

8.1-8.4