Prof: | Robert L. Wolpert |
rlw@duke.edu | OH: Mon 3:30-5:00pm, 211c Old Chem | ||

TA: | Sayan Patra |
sayan.patra@duke.edu |
OH: Tue 6:00-8:00pm, 203 Old Chem | ||

Class: | Tue/Thu 1:25-2:40pm, 127 Soc Psych | ||||

Text: | Sidney Resnick, | A Probability Path | 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, $33, free on-line) | |||

Jacod & Protter, | Probability Essentials (2/e) | (easier than Resnick, $53) | |||

Rick Durrett, | Probability Theory & Examples (4.1/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 ('15, '16, '17) | 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 ('15, '16, '17) | Hists: | Exam, Course |

Nov 19- | Introduction to Martingales (a, b) | hw11 | Nov 28 |

--- Thanksgiving Recess (Nov 20-25) --- | |||

Nov 26-28 | Heavy tails and Extreme Values & More Martingales | ||

Dec 10 | Final Exam Review Session: Loc TBD, 1:25-2:40 | ||

Dec 17 | 2:00-5:00pm Mon: In-class Final Exam ('15, '16, '17) | 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.

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). Avoid using
proof-by-contradiction wherever possible. 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, *TBD**@duke.edu*).
Homeworks assigned the week before midterm exams are collected on Monday
instead of Wednesday, so I can answer questions about them before the exam.

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 2015: | 1st Midterm | 2nd Midterm | Final Exam | ||||
---|---|---|---|---|---|---|---|

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

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

- There are enough seats in the room, and
- They are willing to commit to active participation:
- turn in about a third or so 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.