Prof: | Robert L. Wolpert |
wolpert@stat.duke.edu | OH: Mon 4:30-5:30pm, 211c Old Chem | ||

TAs: | James Johndrow |
jej17@stat.duke.edu | OH: Wed 5:00-6:30pm, 025 Old Chem | ||

Frank Li |
jl494@duke.edu | OH: Tue 6:00-7:15pm, 025 Old Chem | |||

Class: | Tue/Thu 11:45a-1:00p, 311 Soc Sci | ||||

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, $36) | |||

Rick Durrett, | Probability Theory & Examples (4/e) | (more complete) |

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 | Jean Jacod seminar in Soc/Psy 127 | ||

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

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

Sep 24-26 | Inequalities, Independence, & Zero-one Laws | hw5 | Oct 03 |

Oct 01-03 | Review & in-class Midterm Exam I | Hists: | Exam, Course |

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

Oct 08-10 | Convergence: a.s., pr., L_{p},
L_{oo}. UI. |
hw6 | Oct 24 |

--- Fall Break (Oct 12-15) --- | |||

Oct -17 | Expectation Inequalities | ||

Oct 22-24 | Strong & Weak Laws of Large Numbers | hw7 | Oct 31 |

Oct 29-31 | Fourier Theory and the Central Limit Theorem | hw8 | Nov 07 |

III. Conditional Probability &
Conditional Expectations | |||

Nov 05-07 | Cond'l Expectations & the Radon-Nikodym thm | hw9 | Nov 21 |

Nov 12-14 | Review & in-class Midterm Exam II | Hists: | Exam, Course |

Nov 19-21 | Introduction to Martingales (a, b) | hw10 | Dec 03 |

Nov 26 | Heavy tails and Extreme Values | ||

--- Thanksgiving Break (Nov 27-Dec 1) --- | |||

Dec 03 | Review for Final Exam | ||

Dec 10 | 9am-12n Tue: In-class Final Exam ('12) | 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 diagnostic
analysis 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: F09 vsn
(somewhat more advanced than Math 431, Advanced
Calculus I) before taking this course. It is also possible to learn
the background material by working through one of the standard texts (like
the two 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 occuring probability distributions (here is a list of many of them).

Some weeks will have lecture notes added (click on the "Week" column 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).

In-class Midterm and Final examinations are closed-book and closed-notes with one 8½"×11" sheet of your own notes permitted. Tests from a recent STA711 offering 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 |
---|

- 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 either the final exam or a midterm
- 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 plagiarising 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.