**Instructor:** **Alexander Barg,** Professor, Department of Electrical and Computer Engineering

Office: 2361 A.V.Williams Building

Tel. (301) 405 7135

E-mail abarg@umd.edu

**Teaching Assistant:** Arda Aydin

E-mail aaydin@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.

**Class Schedule:**

Lectures: TuTh 9:30-10:45 EGR0108

Discussion: F 11:00-11:50 EGR2116

Instructor office hours: Wed 2:00-3:00, AVW 2361

TA office hours: Friday 9:00-10:50, AVW 1109-A

**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:** 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):

- Exams are closed-book, no calculators or other electronic devices. You can bring one letter-size sheet of notes to any exam, you may write on both sides.
- All exams are cumulative.
- No calculators please.

**Grading Policy:** Homework 10%, Exams: 20% for the lowest-score exam, 30% for second lowest, 40% for the highest score.

Deadline for submitting completed homeworks is stated on each assignment (typically one week after the day they were assigned if not indicated otherwise). Late papers will not be accepted.

A subset of problems from each assignment will be graded. For instance, for a homework of 6 problems I may decide to grade 3 solutions. You are expected to submit solutions of all the problems. If not all the solutions are submitted, your credit for this homework will be reduced proportionally. For instance, if 4 out of 6 problems were attempted, the 100% credit will be multiplied by (2/3).

Lect. # | Topics | Textbook | HW | Solutions | more refs | |
---|---|---|---|---|---|---|

1 (8/30) | Introduction to probability. Notation. Sample spaces. | 1.1, 1.2 | HW1 | Solutions | ||

2 (9/1) | Counting in finite sample spaces | 1.4,1.5 | ||||

3 (9/6) | Definition of probability | 1.3,1.6,1.7 | HW2 | Solutions | ||

4 (9/8) | Conditional probability. Law of total probability. Bayes Rule | 2.1-2.3 | ||||

5 (9/13) | Independence of events; more on conditioning | 2.4-2.6 | ||||

6 (9/15) | Random variables, distribution law, PMFs | 3.1,3.2 | HW3 | Solutions | ||

7 (9/20) | Bernoulli, Binomial, Discrete uniform RVs, Geometric, hypergeometric RVs. | 3.3,3.5 | ||||

8 (9/22) | Cumulative distribution function (CDF). Functions of RVs. | 3.4, 3.6, 3.7 | HW4 | Solutions | ||

9 (9/27) | Independence and conditional independence of RVs. Expectation of an RV. | 3.8,4.1,4.2 | ||||

10 (9/29) | Linearity of expectation. ${\mathbb E}X$ for discrete RVs $X$ (binomial, geometric etc.). | 4.2,4.3 | ||||

11 (10/4) | Indicator RVs and expectation. LOTUS | 4.4, 4.5 | ||||

12 (10/6) | Variance of an RV, examples. Poisson distribution | 4.6, 4.7 | ||||

(10/11) | Midterm 1 |
|||||

13 (10/13) | Poisson and Binomial distributions | 4.7, 4.8 | HW5 | Solutions | ||

14 (10/18) | Continuous RVs. PDF. Uniform distribution. | 5.1, 5.2 | ||||

15 (10/20) | Uniform distribution (cont'd). Normal (Gaussian) distribution. | 5.3, 5.4 | HW6 | Solutions | ||

16 (10/25) | Normal RV. Exponential RV. | 5.4, 5.5 | ||||

17 (10/27) | Poisson process. Moments, sample moments. | 5.6; 6.1-6.3 | HW7 | Solutions | ||

18 (11/1) | Moment generating functions and their uses | 6.4, 6.5 | ||||

19 (11/3) | Joint, marginal, and conditional distributions (discrete and continuous) | 7.1, 7.2 | ||||

20 (11/8) | Joint, marginal, and conditional distributions. | 7.2 | ||||

(11/10) | Midterm 2 |
|||||

21 (11/15) | Covariance and correlation. Examples of multidimensional distributions | 7.3 | ||||

26 (11/17) | Transformations of RVs | 7.4, 7.5, 8.1 | HW8 | Solutions | ||

23 (11/22) | Transformations of multiple RVs. Convolutions. Beta distribution. | 8.1, 8.2, 8.3 | ||||

24 (11/29) | Conditional expectation | 9.1 | ||||

25 (12/1) | Conditional expectation | 9.2, 9.3, 9.5, 9.6 | HW9 | Solutions | ||

26 (12/6) | Inequalities | 10.1, 10.2 | ||||

27 (12/8) | Law of Large Numbers, CLT | 10.2,10.3 | ||||

12/15 | FINAL EXAM: Thu Dec. 15 8:00-10:00 |

** Sample exams:**
*Midterm1* | 1 | 2 |
3 | 4 |
*Midterm2* | 1 | 2 |
3 | 4 |
*Final* | 1 | 2 | 3 |
4 | 5 | 6 |

Home assignments from *earlier installments* of this
class (for your information only):

2019 Spring: | 1 | 2 | 3 | 4 |
5 | 6 | 7 | 8 |
9 | Solutions

2016 Fall: | 1 | 2 | 3 | 4 |
5 | 6 | 7 | 8 | 9 | Solutions

2016 Spring: | 1 | 2 | 3 | 4 |
5 | 6 | 7 | 8 | 9 |
Solutions

2015: | 1 | 2 | 3 | 4 |
5 | 6 | 7 | 8 | 9 | Solutions

Earlier: 1 | 2 | 3 | 4 |
5 | 6 | 7 | 8 | Some solutions