Prof: | Greg Malen | Office: Physics 031, |
gmalen@math.duke.edu |

Class: | T/Th 4:40-5:55pm | Soc/Psych 126 | |

The course text is Jim Pitman, Probability. You will also have access to Elementary Probability for Applications by Rick Durrett on Sakai.

In the syllabus below I have posted for each lecture what section in Pitman or Durrett the material is covered in. I have also posted in the syllabus below links to video lectures by Jonathan Mattingly and Joe Blitzstein that cover the lecture material. These are intended as a supplementary resource. You do not need to watch them, but they are very well done and you may find them quite helpful. For each lecture topic (typically one topic will be spread over two classes), I have posted where in both books the material is covered, links to videos covering the material, a short note on the key topics/ideas, and the homework.

Please also note that I have a ** zero tolerance policy for phones in class. ** They are unbelievably distracting to both me and to your peers. If you expect to be bored in class, bring in something intellectually stimulating to do that involves writing so that it looks like you're taking notes (e.g. sudoku, a crossword puzzle, etc...).

For full credit on homework assignments and exams, ** numerical answers ** should be given either as fractions in lowest terms (2/3, not 17/51), or as decimals to four significant places (0.6666 or 0.6667, not 0.6 or 0.7), not as expressions still in need of evaluation (like $elog\; 2-0.25log85$ or $\sum $_{n≥ 1} (2/5)^{ n}), even if they are correct.

If you are enrolled in 730, you will have an additional assignment which will be to write an essay relating the course material to your own research or work. The homework and exam scores will be reported through Sakai.

Every homework assignment is weighted the same, and your lowest homework score will be dropped. Late work will receive no credit. Even if you have an excused absence or use a STINF, you must turn in your homework. If you are a grad-level student enrolled in 730, there will be an additional assignment towards the end of the semester where you will be required to write an essay connecting probability to your field.

- (Aug 27, 29) Outcomes and events:
- Key ideas
- Chapter 1.1-1.3 in Pitman
- Chapter 1.1-1.2 in Durrett
- Video lectures by Blitzstein Lecture 1: 14:30-End Lecture 3: 17:15-End
- Video lectures by Mattingly Outcome space and events, Partitions and rules of probability
- Extra Problems: Drawing Hearts, Defective Machines, High Card Wins, Taking Classes, Poker Hands
- Homework: Assignment 1
- (Sept 3, 5) Conditional probability:
- Key ideas
- Chapter 1.4-1.6 in Pitman
- Chapter 6 in Durrett
- Video lectures by Blitzstein Lecture 4 Lecture 5
- Video lectures by Mattingly Conditional probability Bayes rule Total probability
- Homework: Assignment 2
- (Sept 10, 12) Distributions I: Binomial, Poisson, Normal:
- Key ideas
- Chapter 2.1-2.4, 1.6 in Pitman
- Chapter 2 and 5.1 in Durrett
- Video lectures by Blitzstein Lecture 8 Lecture 11 Lecture 13
- Video lectures by Mattingly Distributions Binomial I Binomial II Poisson approximation
- Homework: Assignment 3
- (Sept 17, 19) Distributions II: Hypergeometric, Multinomial, Counting:
- Key ideas
- Chapter 2.1, 2.5, 1.6 in Pitman
- Chapter 2 in Durrett
- Video lectures by Blitzstein Lecture 2 Lecture 20
- Video lectures by Mattingly Counting 1 Counting 2 Geometric
- Homework: Assignment 4
- (Sept 24, 26) Random variables: Expectations, Variances, Moments:
- Key ideas
- Chapter 3.2-3.4 in Pitman
- Chapter 3.1 and 4.1-4.3 in Durrett
- Video lectures by Blitzstein Lecture 8 Lecture 9 Lecture 10
- Video lectures by Mattingly Continuous random variables Uniform random variables Scaling and standardizing
- Homework: Assignment 5
- (Oct 1) Review
- (Oct 3) Exam 1
- (Oct 10, Oct 15) Continuous random variables: Cummulative distributions, Probability densities, Change of variables, Order statistics:
- Key ideas
- Chapter 4 in Pitman
- Chapter 3.1-3.3 in Durrett
- Video lectures by Blitzstein Lecture 14 Lecture 25
- Video lectures by Mattingly Uniform random variables Scaling and standardizing
- Homework: Assignment 6
- (Oct 17, 22, 24) Joint distributions: Marginals, Covariance, and Correlation
- Key ideas
- Chapter 5, 6.4, and 6.5 in Pitman
- Chapter 3.4 and 4.4 in Durrett
- Video lectures by Blitzstein Lecture 19 Lecture 21
- Homework: Assignment 7
- (Oct 29, 31) Conditional distributions and expectations:
- Key ideas
- Chapter 6.1-6.3 in Pitman
- Chapter 6.4 in Durrett
- Video lectures by Blitzstein Lecture 25 Lecture 26 Lecture 27
- Homework: Assignment 8
- (Nov 5) Review
- (Nov 7) Exam 2
- (Nov 12, 14) Law of large numbers:
- Key ideas
- Chapter 2.2 and 3.3 in Pitman
- Chapter 4.5 in Durrett
- Supplmental notes
- Video lectures by Blitzstein Lecture 29
- Video lectures by Mattingly Binomial law of large numbers
- Homework: Assignment 9
- (Nov 19, 21) Central limit theorem:
- Key ideas
- Chapter 2.2 and 3.3 in Pitman
- Chapter 5 in Durrett
- Video lectures by Blitzstein Lecture 30
- Video lectures by Mattingly Binomial central limit theorm Central limit theorm
- Homework: Assignment 10
- (Nov 26) Exam 3
- (Dec 3, 5) Markov chains:
- Key ideas
- Chapter in 7 Durrett
- Video lectures by Blitzstein Lecture 31 Lecture 32 Lecture 33
- Final exam: December 11th, 2-5pm in Soc/Psych 126