STP 421 – Probability
Spring 2012
Instructor: Dr. Jay Taylor, office: PSA 447; phone:
9652641; email: jtaylor@math.asu.edu
Time: Mondays and Wednesdays 3:304:45
Location:
ECG G237
Office Hours: Tuesdays 1:004:00 in PSA 447; also
by appointment.
Text: A First Course in Probability
(8^{th} Edition) by Sheldon Ross. Warning: The 7^{th}
and 8^{th} 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 SelfTest 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 
2.12.4 
11 Jan 
Properties of probabilities; Continuity 
2.6 
16 Jan 
Martin Luther King Jr. Holiday 

18 Jan 
Ordered Samples; Permutations; Combinations 
1.11.4 
23 Jan 
Multinomials; Combinatorial Identities 
1.5 
25 Jan 
Symmetric Probability Spaces 
2.5 
30 Jan 
Conditional Probability 
3.13.2 
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 


15 Feb 
Random variables; discrete distributions 
4.14.2 
20 Feb 
Expectations and variances of discrete distributions 
4.34.5 
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, 5.25.3 
12 March 
Normal distribution 
5.4 
14 March 
Exponential and related distributions 
5.55.6 
19 March 
Spring Break 

21 March 
Spring Break 

26 March 
Functions of RVs. 
5.7 
28 March 
Joint distributions; Independent RVs. Exam 2 distributed. 
6.16.2 
2 April 
Sums of independent RVs; Convolutions. Exam 2 collected (Solutions). 
6.3 
4 April 
Conditional distributions 
6.46.5 
9 April 
Expectations of sums 
7.17.2 
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 
8.18.4 