Prof: | Robert L. Wolpert |
rlw@duke.edu | OH: Mon 1:30–3, 211C Old Chem | ||

TAs: | Felipe Ossa |
felipe.ossa@duke.edu |
OH: Mon 6–7:30, 203B Old Chem | ||

& | Andy McCormack |
andrew.mccormack@duke.edu |
OH: Wed 4–5:30, 203B Old Chem | ||

& | Azeem Zaman |
azeem.zaman@duke.edu |
OH: Tue 12–1:30, 203B Old Chem | ||

Class: | Tue/Thu 1:25–2:40pm, D-106 LSRC | ||||

Text: | Sidney Resnick, | A Probability Path (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) |

Week | Topic | Homework | |
---|---|---|---|

I. Foundations of Probability |
Problems | Due | |

Aug 27-29 | Probability spaces: Sets, Events, and σ-Fields | hw1 | Sep 05 |

Sep 03-05 | Construction & extension of Measures | hw2 | Sep 12 |

Sep 10-12 | Random variables and their Distributions | hw3 | Sep 19 |

Sep 17-19 | Expectation & the Lebesgue Theorems | hw4 | Sep 26 |

Sep 24-26 | Expect'n Ineqs, L_{p} Spaces, & Independence |
hw5 | Oct 01 |

Oct 01-03 | Review & in-class Midterm Exam I ('16, '17, '18) | Hists: | Exam, Course |

--- Fall Break (Oct 07-09) --- | |||

Oct -10 | Zero-one Laws & Hoeffding's Inequality | hw6 | Oct 17 |

II. Convergence of Random Variables and
Distributions | |||

Oct 15-17 | Convergence: a.s., pr., L_{p},
L_{∞}, UI. |
hw7 | Oct 24 |

Oct 22-24 | Laws of Large Numbers, Strong & Weak | hw8 | Oct 31 |

Oct 29-31 | Fourier Theory and the Central Limit Theorem | hw9 | Nov 07 |

III. Conditional Probability &
Conditional Expectations | |||

Nov 05-07 | Cond'l Expectations & the Radon-Nikodym thm | hw10 | Nov 12 |

Nov 12-14 | Review & in-class Midterm Exam II ('16, '17, '18) | Hists: | Exam, Course |

Nov 19-21 | Intro to Martingales (Optional: a, b) | hw11 | Nov 26 |

Nov 26 | Extremes (Bovier Notes) | ||

--- TG Recess + Grad Reading Pd (Nov 27-Dec 10) --- | |||

Dec 12-13 | Informal office-hours most of day | ||

Dec 14 | 2:00-5:00pm Sat: In-class Final Exam ('16, '17, '18) | 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 R^{n},
convergence in metric spaces (especially uniform convergence of functions on
R^{n}), 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 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.

Homeworks may be submitted in paper form (just bring them to class on
Thursday) or, if necessary (for example, if you're out of town on the
due date), electronically in the form of pdf files submitted as Sakai
"Assignments" or sent by e-mail to the course TAs,
Felipe,
Andy and
Azeem. 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,
not a phone camera (there are scanners in Bostock); send a single PDF file,
not JPGs; and 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 collected on Thursday at the start of class, and returned the following Tuesday. Homeworks assigned the week before exams are collected 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.

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 2016: | 1st Midterm | 2nd Midterm | Final Exam | |||||||
---|---|---|---|---|---|---|---|---|---|---|

Fall 2017: | 1st Midterm | 2nd Midterm | Final Exam | |||||||

Fall 2018: | 1st Midterm | 2nd Midterm | Final Exam |

- There are enough seats in the room, and
- They are willing to commit to active participation:
- turn in several of the homeworks (or a few problems on each of most HW assignments),
- take one of the midterms or the final exam,
- come regularly to lectures, and ask or answer questions now and then.

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.