Instructor: Alexander Barg, Professor, Department of Electrical and Computer Engineering
Office: 2361 A.V.Williams Building
E-mail abarg@umd.edu
Teaching Assistant: Weihang Cao
E-mail whcao@umd.edu
Course communication: will be through this web page and e-mail using the e-mail addresses of students registered in the university system. I expect you to view this page and read your e-mail at least once a week in order not to miss important announcements, postings of home assignments as well as other information. Lecture notes will be posted to Canvas.
The best way to reach me is by email using the above address. Please do not send me messages on Canvas as I do not follow them regularly.Class Schedule:
Lectures: MW 2:00 - 3:15pm, AJC 2132
Discussion: Sec.0102 F 10:00-10:50 MTH B0423; Sec.0101: F 11:00-11:50 MTH0303
Instructor soffice hours: Wed 12:00-1:30, AVW 2361
TA office hours: Tue 10am-12pm, AVW 1111
Textbook: Joseph Blitzstein and Jessica Hwang, Introduction to Probability, 2nd edition, 2019, ISBN 9781138369917 (required)
Web site of the book with access to a free online copy, youtube lectures by the J. Blitzstein
following the book (not required) and other materials.
Other useful books:
Santosh Venkatesh, Theory of Probability, Cambridge University Press 2013
Sheldon Ross, A First Course in Probability, Prentice Hall.
Prerequisites: 1st year calculus. See Appendix A in the textbook. Click here for a sample of questions.
Examinations: Two midterm exams and one final.
Exam regulations (these rules apply to each of the three exams):
Grading Policy: Homework 10%, Max(midterm1, midterm2) 30%, Min(midterm1,midterm2) 20%, final 40%
Home assignments: There will be 8-9 assignments. HW dates are tentative and may change; please check back. Please upload your solutions to Canvas by the deadline. Email and paper submissions not accepted.| Lect. # | Topics | Textbook | HW | Solutions | more refs | |
|---|---|---|---|---|---|---|
| 1 (9/3) | Introduction to probability. Notation. Sample spaces. | 1.1, 1.2 | HW1 | Solutions | ||
| 2 (9/8) | Counting in finite sample spaces | 1.4,1.5 | ||||
| 3 (9/10) | Definition of probability | 1.3,1.6,1.7 | ||||
| 4 (9/15) | Conditional probability. Law of total probability. Bayes Rule | 2.1-2.3 | HW2 | Solutions | ||
| 5 (9/17) | Independence of events; more on conditioning | 2.4-2.6 | ||||
| 6 (9/22) | Random variables, distribution law, PMFs | 3.1,3.2 | ||||
| 7 (9/24) | Bernoulli, Binomial, Discrete uniform RVs, Geometric, hypergeometric RVs. | 3.3,3.5 | ||||
| 8 (9/29) | Cumulative distribution function (CDF). Functions of RVs. | 3.4, 3.6, 3.7 | HW3 | Solutions | ||
| 9 (10/1) | Independence and conditional independence of RVs. Expectation of an RV. | 3.8,4.1,4.2 | ||||
| 10 (10/6) | Linearity of expectation. ${\mathbb E}X$ for discrete RVs $X$ (binomial, geometric etc.). | 4.2,4.3 | HW4 | Solutions | ||
| 11 (10/8) | Indicator RVs and expectation. LOTUS | 4.4, 4.5 | ||||
| (10/13) | Fall break, no class | |||||
| 12 (10/15) | Variance of an RV, examples. Poisson distribution | 4.6, 4.7 | ||||
| (10/20) | Midterm 1 | Topics covered | ||||
| 13 (10/22) | Poisson and Binomial distributions | 4.7, 4.8 | HW5 | |||
| 14 (10/27) | Continuous RVs. PDF. Uniform distribution. | 5.1, 5.2 | ||||
| 15 (10/29) | Uniform distribution (cont'd). Normal (Gaussian) distribution. | 5.3, 5.4 | HW6 | |||
| 16 (11/3) | Normal RV. Exponential RV. | 5.4, 5.5 | ||||
| 17 (11/5) | Poisson process. Moments, sample moments. | 5.6; 6.1-6.3 | HW7 | |||
| 18 (11/10) | Moment generating functions and their uses | 6.4, 6.5 | ||||
| 19 (11/12) | Joint, marginal, and conditional distributions (discrete and continuous) | 7.1, 7.2 | ||||
| 20 (11/17) | Joint, marginal, and conditional distributions. | 7.2 | ||||
| (11/19) | Midterm 2 | Topics covered | ||||
| 21 (11/24) | Covariance and correlation. Examples of multidimensional distributions | 7.3 | ||||
| 11/26 | Thanksgiving, no class | 7.3 | ||||
| 22 (12/1) | Transformations of RVs | 7.4, 7.5, 8.1 | HW8 | |||
| 23 (12/3) | Transformations of multiple RVs. Convolutions. Beta distribution. | 8.1, 8.2, 8.3 | ||||
| 24 (12/8) | Conditional expectation | 9.1 | ||||
| 25 (12/10) | Conditional expectation | 9.2, 9.3, 9.5, 9.6 | HW9 | |||
| 12/15 | FINAL EXAM: TBD |