|Prof:||Robert L. Wolpertfirstname.lastname@example.org||OH: Fri 12:15-1:15pm, 211c Old Chem|
|TA:||Lu Wangemail@example.com||OH: Tue 7:00-9:00pm, 211a Old Chem|
|Class:||Mon/Wed 1:25p-2:40p, 311 Soc Science|
|Text:||Sidney Resnick,||A Probability Path||Additional references|
|Opt'l:||Patrick Billingsley,||Probability and Measure (3/e)||(a classic)|
|Jacod & Protter,||Probability Essentials (2/e)||(easier than Resnick, $40)|
|Rick Durrett,||Probability Theory & Examples (4/e)||(more complete)|
|I. Foundations of Probability||Problems||Due|
|Aug 24-26||Probability spaces: Sets, Events, and σ-Fields||hw1||Sep 02|
|Aug 31-02||Construction & extension of Measures||hw2||Sep 09|
|Sep 07-09||Random variables and their Distributions||hw3||Sep 16|
|Sep 14-16||Expectation & the Lebesgue Theorems||hw4||Sep 23|
|Sep 21-23||Expectation Inequalities||hw5||Sep 28|
|Sep 28-30||Review & in-class Midterm Exam I ('12, '13, '14)||Hists:||Exam, Course|
|Oct 06-08||Independence & Zero-one Laws||hw6||Oct 21|
|--- Fall Break (Oct 10-13) ---|
|II. Convergence of Random Variables and Distributions|
|Oct -14||Convergence: a.s., pr., Lp, Loo, UI.||hw7||Oct 28|
|Oct 19-21||Laws of Large Numbers, Strong & Weak||hw8||Nov 04|
|Oct 26-28||Fourier Theory and the Central Limit Theorem||hw9||Nov 09|
|III. Conditional Probability & Conditional Expectations|
|Nov 02-04||Cond'l Expectations & the Radon-Nikodym thm||hw10||Nov 23|
|Nov 09-11||Review & in-class Midterm Exam II ('12, '13, '14)||Hists:||Exam, Course|
|Nov 16-18||Introduction to Martingales (a, b)|
|Nov 23||Heavy tails and Extreme Values|
|--- Thanksgiving Recess (Nov 25-29) ---|
|Dec 07||Review for Final Exam, Mon 1:25-2:40|
|Dec 12||2-5pm Sat: In-class Final Exam ('12, '13, '14)||Hists: exam, course|
Students are expected to be well-versed in real analysis at the level of W. Rudin's Principles of Mathematical Analysis or M. Reed's Fundamental Ideas of Analysis— the topology of Rn, convergence in metric spaces (especially uniform convergence of functions on Rn), infinite series, countable and uncountable sets, compactness and convexity, and so forth. Try to answer the questions on this analysis diagnostic quiz to see if you're prepared. Most students who majored in mathematics as undergraduates will be familiar with this material, but students with less background in math should consider taking Duke's Math 531, Basic Analysis I (somewhat more advanced than Math 431, Advanced Calculus I, but that's a good second choice) before taking this course. It is also possible to learn the background material by working through one of the standard texts (like Rudin's or Reed's books listed above) and doing most of the problems, preferably in collaboration with a couple of other students and with a faculty member (maybe me) to help out now and then. More advanced mathematical topics from real analysis, including parts of measure theory, Fourier and functional analysis, are introduced as needed to support a deep understanding of probability and its applications. Topics of later interest in statistics (e.g., regular conditional density functions) are given special attention, while those of lesser statistical interest may be omitted.
Most students in the class will be familiar with undergraduate-level probability at the level of STA 230. While this isn't required, students should be or become familiar with the usual commonly occurring probability distributions (here is a list of many of them).
Most weeks will have lecture notes added (click on the "Week" column above if it's blue or green). This is syllabus is tentative, last revised , and will almost surely be superseded— reload your browser for the current version.
Homework problems are awarded zero to three points each, based on your success in communicating a correct solution. For the full three points the solution must be clear, concise, and correct; even a correct solution will lose points or be returned ungraded if it is not clear and concise. Neatness counts. Consider using LaTeX and submitting your work in pdf form if necessary (it's good practice anyway). Homeworks may be submitted in paper form (just bring them to class on Wednesday) or electronically in the form of pdf files (submit as Sakai "Assignments" or send by e-mail to the course TA, firstname.lastname@example.org).
In-class Midterm and Final examinations are closed-book and closed-notes with one 8½"×11" sheet of your own notes permitted. Tests from recent STA711 offerings are available to help you know what to expect and to help you prepare for this year's tests:
|Fall 2012:||1st Midterm||2nd Midterm||Final Exam|
|Fall 2013:||1st Midterm||2nd Midterm||Final Exam|
|Fall 2014:||1st Midterm||2nd Midterm||Final Exam|
You may discuss and collaborate in solving homework problems, but you may not copy— each student should write up his or her solution. Cheating on exams, copying or plagiarizing homeworks or projects, lying about an illness or absence and other forms of academic dishonesty are a breach of trust with classmates and faculty, and will not be tolerated. They also violate Duke's Community Standard and will be referred to the Graduate School Judicial Board or the Dean of the Graduate School.