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

TA: | T B A |
tba@stat.duke.edu | OH: Wed 6:00-7:30pm, 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 | (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 Meeting: Massive Datasets | ||

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

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

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

Oct 02-04 | Convergence concepts: a.s., i.p., L_{p},
L_{oo} |
hw6 | Oct 11 |

Oct 09-11 | Uniform Integrability | hw7 | Oct 18 |

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

Oct 18 | Review & in-class Midterm Exam (Thu Oct 20) | '10, '11 | Results |

Oct 23-25 | Strong & Weak Laws of Large Numbers | hw8 | Nov 01 |

II. Convergence of Distributions | |||

Oct 30-01 | Convergence in Dist'n, CLT, & Stable Limits | hw9 | Nov 08 |

Nov 06-08 | Extremes (notes) | hw10 | Nov 15 |

III. Conditional Probability & Expectation | |||

Nov 13-15 | Radon-Nikodym thm and conditional probability | hw11 | Nov 20 |

Nov 20 | Stein's Method (time permitting) | ||

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

Nov 27-29 | Martingales and Markov Chains | ||

Dec 13 | Take-home Final Exam due 9am ('07, '10, '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 will be familiar with this material;
but students with less background in math should consider taking Duke's Math 531 (203), Basic
Analysis I: F09 vsn
before taking this course. It is also possible to learn the material by
working through one of the standard texts 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.

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.

Course grade is based on homework (20%), in-class midterm exam (40%), and take-home final exam (40%).

Unregistered students are welcome to sit in on or (preferably) audit a course if:

- 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.