## MATH/STA 230 (and 730): Probability, Fall 2019

 Prof: Greg Malen Office: Physics 031, gmalen@math.duke.edu Class: T/Th 4:40-5:55pm Soc/Psych 126

### Description

This is a basic calculus-based first course in the theory and application of probability. It develops quantitative methods for solving problems that involve uncertainty, and provides a foundation for the further study of statistics or random processes. Many probability calculations are based on summing infinite series or on evaluating integrals. If you are unsure about your calculus preparation, try this diagnostic quiz.

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...).

### Homework

Each homework assignment will be due at the start of the next topic, e.g. Assignment 1 is due on Sept 3th, and so on. This will not always be a Tuesday or always a Thursday, because life is not always that simple. You may work with other students on the homework problems, but your final answers should be written up independently: copying homework solutions is not allowed. You are encouraged to ask the professor and the TAs in the help-room for help on your homework (in person or by e-mail), after you have tried to solve the problems on your own.

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.

The course grade is based on three midterms (20%, 20%, and 20%, respectively), homeworks (10%), and a final exam (30%). The exams are in class and closed books; you will be allowed to bring in a single sheet of handwritten notes and formulas. Make-up exams will only be given in extraordinary situations. You cannot pass the class if you do not take the final.

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.

### Syllabus

1. (Aug 27, 29) Outcomes and events:

2. (Sept 3, 5) Conditional probability:

3. (Sept 10, 12) Distributions I: Binomial, Poisson, Normal:

4. (Sept 17, 19) Distributions II: Hypergeometric, Multinomial, Counting:

5. (Sept 24, 26) Random variables: Expectations, Variances, Moments:

6. (Oct 1) Review

7. (Oct 3) Exam 1

8. (Oct 10, Oct 15) Continuous random variables: Cummulative distributions, Probability densities, Change of variables, Order statistics:

9. (Oct 17, 22, 24) Joint distributions: Marginals, Covariance, and Correlation

10. (Oct 29, 31) Conditional distributions and expectations:

11. (Nov 5) Review

12. (Nov 7) Exam 2

13. (Nov 12, 14) Law of large numbers:

14. (Nov 19, 21) Central limit theorem:

15. (Nov 26) Exam 3

16. (Dec 3, 5) Markov chains:

17. Final exam: December 11th, 2-5pm in Soc/Psych 126