STP 421 – Probability
Fall 2013
Instructor: Dr. Jay Taylor, office: PSA 447; phone:
9652641; email: jtaylor@math.asu.edu
Time: Mondays and Wednesdays 3:004:15
Location:
PABLO 105
Office Hours: Wednesdays 12:002:00 in PSA 447;
also by appointment.
Text: Principles of Uncertainty
by
Joseph Kadane (Chapman & Hall, 2011). A pdf copy of this text is
available (legally) at the following link.
You can also purchase a hard copy through Amazon.com or CRC Press.
Course Description: This course will provide an introduction to probability theory that emphasizes the statistical applications of this subject, particularly those relevant to Bayesian inference. Topics covered will include coherence and the laws of probability, conditional distributions and Bayes' formula, random variables, discrete and continuous distributions, stochastic simulation, univariate and multivariate normal distributions, and the fundamental limit theorems of probability theory. Where possible, examples of applications of probability to realworld problems will be given.
Prerequisites: Three semesters of calculus, including vector calculus. Although we will cover some proofs in lectures, it is not necessary to have taken MAT 300 (Mathematical Structures) to do well in this course. However, you should be familiar with elementary set theory (unions, intersections, complements, etc.) and it is essential that you be able to carry out the kinds of calculations covered in college algebra and calculus courses. Please review these subjects if your mastery of them is rusty.
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: Problem sets will usually not be accepted after the solutions have been posted except when there are extenuating circumstances such as illness.) You are welcome to work in groups, but you should write up your solutions individually and you should always give due credit if your solution came from another source, such as a text book, from an online resource, or from one of your classmates. Solutions should either be typed or neatly written. Because mathematics is best learned by attempting to solve problems, it is very important that you attempt every problem set, no matter how difficult, and turn in solutions, even if they are partial or incorrect.
Quizzes: There will be weekly quizzes, usually consisting of a single question/problem and lasting 5 minutes or less. These will be unannounced and cannot be made up except in the case of an emergency. However, I will drop your four lowest scores, which means that you can miss four of these without incurring a penalty.
Exams: There will be two exams, including a takehome midterm that will be distributed in early October and an inclass final exam (date TBA).
Grading and Assignments: Grades will be based on your cumulative score on the exams (100 points each), quizzes (100 points in total), and problems sets (200 points in total). Of the 500 points possible, 450 points and above will guarantee an A, 400 points and above will guarantee a B, 350 points and above will guarantee a C, and 300 points and above will guarantee a D.
Syllabus:
Date 
Topic 
Reading 
26 Aug 
Overview; Coherence and probability 
Kad 1.11.2; slides 
28 Aug 
Probabilities of unions 
Kad 1.3 
2 Sept 
Labor Day – no class 

4 Sept 
Random variables with finitely many values 
Kad 1.41.5 
9 Sept 
Properties of expectations; Coherence prevents sure loss 
Kad 1.61.7 
11 Sept 
Conditional probability; The birthday problem 
Kad 2.12.2; slides 
16 Sept 
Simpson's Paradox; Bayes' theorem and Bayesian statistics 
Kad 2.32.4 
18 Sept 
Independence 
Kad 2.5 
23 Sept 
Gambler's Ruin 
Kad 2.7 
25 Sept 
Iterated expectations; Independence of RVs 
Kad 2.8 
30 Sept 
Binomial, multinomial and hypergeometric distributions 
Kad 2.92.10 
2 Oct 
Variance and covariance 
Kad 2.11 
7 Oct 
Weak Law of Large Numbers 
Kad 2.13 
9 Oct 
Random variables with countably many values; countable additivity 
Kad 3.13.3; slides 
14 Oct 
Fall Break – no class 

16 Oct 
Properties of expectations; Midterm distributed 
Kad 3.4 
21 Oct 
Probability generating functions; Geometric distribution; Midterm due (solutions) 
Kad 3.63.8 
23 Oct 
Poisson distribution 
Kad 3.9 
28 Oct 
Genealogies and coalescents 

30 Oct 
Continuous distributions 
Kad 4.1; slides 
4 Nov 
Measure theory and the Lebesgue integral 
instructor's notes 
6 Nov 
Expectations and integrals 
Kad 4.44.5 
11 Nov 
Veteran's Day – no class 

13 Nov 
Exponential and gamma distributions 
Instructor's notes 
18 Nov 
Joint distributions 
Kad 4.2 
20 Nov 
Conditional distributions 
Kad 4.3 
25 Nov 
Transformations of random variables 
Kad 5.15.3; slides 
27 Nov 
Moment generating functions; characteristic functions 
Kad 6.16.3 
2 Dec 
Normal distributions 
Kad 6.9 
4 Dec 
The Central Limit Theorem 
Kad 6.11 