Prof: | Robert L. Wolpert |
wolpert@stat.duke.edu | OH: Mon 3:00-4:00pm, 211c Old Chem | ||

TA: | Anurag Ghosh |
ag246@stat.duke.edu | OH: Wed 5:30-7:00pm, 211a Old Chem | ||

Class: | Tue/Thu 11:45a-1:00p, 025 Old Chem | ||||

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 28-30 | Probability spaces: Sets, Events, and σ-Fields | hw1 | Sep 06 |

Sep 04-06 | Construction & extension of Measures | hw2 | Sep 13 |

Sep 09-12 | SAMSI Workshop: Massive Datasets | ||

Sep 11-13 | Random variables and their Distributions | hw3 | Sep 20 |

Sep 19-21 | SAMSI Workshop: AstroStats | ||

Sep 18-20 | Expectation & the Lebesgue Theorems | hw4 | Sep 27 |

Sep 25-27 | Inequalities, Independence, & Zero-one Laws | hw5 | Oct 04 |

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

Oct 02-04 | Convergence concepts: a.s., i.p., L_{p},
L_{oo} |
hw6 | Oct 18 |

Oct 09-11 | Review & in-class Midterm Exam I | '10, '11 | Exam, Course |

--- Fall Break (Oct 13-16) --- | |||

Oct -18 | Uniform Integrability | ||

Oct 23-25 | Strong & Weak Laws of Large Numbers | hw7 | Nov 01 |

--- Halloween Break (Oct 30) --- | |||

Nov -01 | Fourier Theory and Convergence in Distribution | hw8 | Nov 08 |

III. Conditional Probability &
Conditional Expectations | |||

Nov 06-08 | Central Limit Theorem & Stable Limit Theorem | hw9 | Nov 20 |

Nov 13-15 | Review & in-class Midterm Exam II | Exam, Course | |

Nov 20 | Radon-Nikodym thm | hw10 | Dec 04 |

--- Thanksgiving Break (Nov 21-26) --- | |||

Nov 27-29 | Conditional probability & Martingales | hw10 | Dec 04 |

Dec 04 | Extremes & Review for Final Exam | ||

Dec 12 | 9am Wed: In-class Final Exam ('07, '10, '11) | 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 (old 203), Basic
Analysis I: F09
vsn (somewhat more advanced than Math 431 (old 139),
Advanced Calculus I) before taking this course. It is also possible to
learn the 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 (old 104). 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.

- There are enough seats in the room,
- S/He is 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 the midterm
- come regularly to lectures, and ask or answer questions now and then.

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 University Judicial Board.