|Prof:||Robert L. Wolpertfirstname.lastname@example.org||OH: Mon 1:30–3, Zoom|
|TAs:||Joseph Lawsonemail@example.com||OH: Wed 4–5:30, Zoom|
|&||Pritam Deyfirstname.lastname@example.org||OH: Tue 12–1:30, Zoom|
|Class:||Tue/Thu 1:45–3:00pm, Zoom|
|Text:||Sidney Resnick,||A Probability Path (free pdf)||Additional references|
|Opt'l:||Patrick Billingsley,||Probability and Measure||(a classic)|
|Jeff Rosenthal,||A First Look at Rigorous Probability Theory (2/e)||(easier than Resnick, and just $33)|
|Jacod & Protter,||Probability Essentials (2/e)||(easier than Resnick, $53)|
|Rick Durrett,||Probability Theory & Examples (5/e)||(more complete, free on-line)|
|I. Foundations of Probability||Problems||Due|
|Aug 18-20||Probability spaces: Sets, Events, and σ-Fields||hw1||Aug 27|
|Aug 25-27||Construction & extension of Measures||hw2||Sep 03|
|Sep 01-03||Random variables and their Distributions||hw3||Sep 10|
|Sep 08-10||Expectation & the Lebesgue Theorems||hw4||Sep 15|
|Sep 15-17||Review & in-class Midterm Exam I ('17, '18, '19)||Hists:||Exam, Course|
|Sep 22-24||Expect'n Ineqs, Lp Spaces, & Independence||hw5||Oct 01|
|Sep 29-01||Zero-one Laws & Hoeffding's Inequality||hw6||Oct 08|
|II. Convergence of Random Variables and Distributions|
|Oct 06-08||Convergence: a.s., pr., Lp, L∞, UI.||hw7||Oct 15|
|Oct 13-15||Laws of Large Numbers, Strong & Weak||hw8||Oct 20|
|Oct 20-22||Review & in-class Midterm Exam II ('17, '18, '19)||Hists:||Exam, Course|
|Oct 27-29||Fourier Theory and the Central Limit Theorem||hw9||Nov 05|
|III. Conditional Probability & Conditional Expectations|
|Nov 03-05||Cond'l Expectations & the Radon-Nikodym thm||hw10||Nov 12|
|Nov 10-12||Intro to Martingales (Optional: a, b)|
|Nov 22||2:00pm-5:00pm Sun: In-class Final Exam ('17, '18, '19)||Hists:||Exam, Course.|
|--- TG (Nov 26), Course Ends ---|
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 MTH 531, Basic Analysis I (somewhat more advanced than MTH 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 = MTH 230, STA 240L, or MTH 340. 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 available (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. Warning: lecture notes and homework problems are also revised from time to time as I try to improve them. SO, it's best not to print out future problem sets or lecture notes until you need them. Lecture notes all have a "last edited" date at the end; homeworks might change any time until the week before they are due.
Homework problems are awarded points (usually up to three, but sometimes four or five) based on your success in communicating a correct solution. For full credit 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 (it's good practice anyway). Avoid using proof-by-contradiction wherever possible— it's too easy to create an errant "contradiction" by making some minor mistake.
Each homework assignment must be submitted as a single PDF document (not word, not images like png or jpg, not separate files for different problems). They may be submitted through Sakai or Gradescope. LaTeX typeset homeworks are much better than scanned hand-written ones. If you must scan a hand-written homework, use pen or a very dark pencil; use a scanner, if you have one, or a good cell-phone scanner--- see suggestions from Gradescope (that page also gives instructions for submission via Gradescope) or the New York Times, for instance. Make sure YOU can read the scanned image before you send it. If you can't read it then we can't either. Adjust brightness or other image parameters if necessary.
Most homeworks are due on Thursday before the start of class, so I can answer questions about their solutions. Typically they are returned by the following Tuesday's class. Homeworks assigned the week before exams are due on Tuesday instead of Thursday, so I can answer questions about them before the exam. Remember, homework problems are subject to change up to a week before the due-date.
Midterm and Final examinations are open-book and open-notes, but you should not search for answers on-line during the exam. 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 2017:||1st Midterm||2nd Midterm||Final Exam|
|Fall 2018:||1st Midterm||2nd Midterm||Final Exam|
|Fall 2019:||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. Additionally, there may be penalties to your final course grade. Please review Duke's Standards of Conduct.