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| Day/Time: | TuTh 12:30pm -- 1:45pm EST |
| Location: | Kim Engineering Building (KEB) -- Room 1110 |
| Armand M. MAKOWSKI | |
| Office: | AVW - 2357 |
| Voice: | (301) 405 - 6844 |
| Fax: | (301) 314 - 9281 |
| Email: | armand@umd.edu |
| Day/Time: | TuTh 10:00am -- 11:30pm EST |
| Also by appointment (on zoom if needed). Just contact me by email! |
The lectures will be based on a set of Lecture Notes that will be posted online, and updated regularly in the course of the semester. However, the following textbooks provide an excelent coverage of the material that will be discussed in this class.
| Recommended text: | Bruce HAJEK |
| (Suggested) | Random Processes for Engineers, |
| Cambridge University Press, Cambridge (UK), 2015. | |
| Prepublication version available online | |
| Suggested text (See below): | Geoffrey R. GRIMMETT and David R. STIRZAKER |
| One Thousand Exercises in Probability -- With solutions! | |
| Oxford University Press, Oxford (UK), 2001. |
Additional material and information can be found in the following books and references with coverage similar or complementary to the one given in this course
| Patrick BILLINGSLEY, Probability and Measure (3rd Edition), Wiley-Interscience, 1995. | |
| Kai Lai CHUNG, A Course in Probability Theory (Revised Edition, 2nd Edition), Academic Press, 2000. | |
| Geoffrey R. GRIMMETT and David R. STIRZAKER, Probability and Random Processes (Third Edition), Oxford University Press, Oxford (UK), 2001. | |
| Sheldon M. ROSS, A First Course in Probability (6th Edition), Prentice-Hall, Upper Saddle River (NJ), 2001. | |
| Sheldon M. ROSS, Introduction to Probability Models (10th Edition), Academic Press, 2009. | |
| Sheldon M. ROSS and Erol A. PEKOZ, A Second Course in Probability, ProbabilityBookstore.com, Boston (MA), 2007. | |
| Santosh S. VENKATESH, The Theory of Probability: Explorations and Applications, Cambridge University Press, Cambridge (UK), 2013. |
Introduction to Probability Theory: Probability models, probability spaces (sigma-fields, probability measures), independence, conditional probabilities (Law of total probability and Bayes' rule), Borel-Cantelli Lemmas
Random variables, probability distributions, expectations (Lebesgue integration, basic definition and properties), conditional expectations (where the conditioning is done with respect to (i) an event, (ii) the sigma-field induced by a partition, (iii) a discrete random variable, and (iv) a general sub-sigma-field)
Characteristic functions, Gaussian rvs
Convergence of sequences of random variables: Almost sure, in probability, in mean-square and in distribution. Definitions, Cauchy criterion, charaterization
Classical limit results of the Theory of Probability: Laws of Large Numbers (LLNs), Central Limit Theorem (CLT) and Poisson Convergence
Some examples of processes: Renewal processes, Stationary processes (wide-sense and strict sense), Markov property, gaussian process, Brownian motion
| ENEE 324: | Engineering Probability (or equivalent) |
Homeworks will be assigned on a weekly basis: The homework assignment for the week will be posted online every Sunday of that week starting 09/03. Each weekly assignment will contain ten (10) homework problems. Many of these problems will come from either the Lecture Notes, from the text by Hajek or from the collection of problems compiled by Grimmett and Stirzaker. The TA will prepare an answer key for each weekly problem set to be made available by Wednesday at the latest, and to be discussed by the TA during that week recitation sessions. You are invited to request by email the problems you may want him to discuss! Homeworks will not be graded.
Click here to see the reading assignments -- To be updated every week on Thursday so that you can prepare for the coming week.
The Lecture Notes are available online in pdf [Version uploaded on 12/15/2022 at 11:52pm], and will be periodically updated. Available so far:
| Chapter 1: | Modeling random experiments |
| Chapter 2: | Elementary Probability Theory |
| Chapter 3: | Limits of probabilities vs. probabilities of limiting events |
| Chapter 4: | Measurable mappings: A tale of sigma-fields |
| Chapter 5: | Constructing (probability) measures: Caratheodory's ideas at work |
| Chapter 6: | Constructing (probability) measures: Extension results and examples |
| Chapter 7: | Random variables and their distributions |
| Chapter 8: | Discrete random variables |
| Chapter 9: | Continuous random variables |
| Chapter 10: | Mathematical expectations: Definitions |
| Chapter 11: | Mathematical expectations (I): Basic properties |
| Chapter 12: | Mathematical expectations (II): Advanced properties |
| Chapter 13: | Moments and inequalities |
| Chapter 14: | Bounding probabilities |
| Chapter 15: | Conditional expectations: The case of partitions |
| Chapter 16: | Conditional expectations: The general case |
| Chapter 17: | Probability distributions and their transforms |
| Chapter 18: | Gaussian random variables |
| Chapter 19: | Convergence of random variables |
| Chapter 20: | From convergence in distribution to weak convergence |
| Chapter 21: | The classical limit theorems |
| Appendix A: | Limits |
| Appendix B: | Sums, series and summation |
A link to a pdf file containing the textbook often used in MATH 630 and MATH 631:
H.L. ROYDEN and P.M. FITZPATRICK, Real Analysis (Fourth Edition), PHI Learning Private Limited (New Delhi, India).
| Name: | Arunabh SRIVASTAVA |
| Email: | arunabh@umd.edu |
| Phone: | |
| Office: | AV Williams 1109 |
| Office hours: | Tu (10:00am - 11:00am) and Th (10:00am - 11:00am) |
| Also by appointment |
| Day/Time: | Thursday (5:00pm - 5:50pm) or Friday (11:00am - 11:50am) | |
| Room: | EGR 3114 or JMP 1202 |
During the recitations, the TA will review some key points of the course material, and the solutions to various exercises (in the problem sets) will be discussed -- See above for additional details.
Starting with the second week of classes, there will be a quizz at the end of each recitation: You will be asked a single question concerning any topic covered up to, and including, the Tuesday lecture of that week. You are allowed to refer to your notes.
Quizzes are tentatively scheduled as follows:
| Th 09/01 or /Fr 09/02: | NO QUIZZ |
| Th 09/08 or /Fr 09/09: | Quizz # 1 |
| Th 09/15 or /Fr 09/16: | Quizz # 2 |
| Th 09/22 or /Fr 09/23: | Quizz # 3 |
| Th 09/29 or Fr 09/30: | NO QUIZZ with Quizz # 4 given instead on Tu 09/27 |
| Th 10/06 or Fr 10/07: | Quizz # 5 |
| Th 10/13 or Fr 10/14 | Quizz # 6 |
| Th 10/20 or Fr 10/21: | Quizz # 7 |
| Th 10/27 or Fr 10/28: | Quizz # 8 |
| Th 11/03 or Fr 11/04: | Quizz # 9 |
| Th 11/10 or Fr 11/11: | Quizz # 10 |
| Th 11/17 or Fr 11/18: | Quizz # 11 |
| Th 11/24 or Fr 11/25: | NO QUIZZ -- THANKSGIVING BREAK |
| Th 12/01 or Fr 12/02: | Quizz # 12 |
| Th 12/08 or Fr 12/09: | NO QUIZZ |
The final grade for the course will be based on your performance on quizzes (taken during recitation periods), two tests and a final exam. All tests and the final exam will be take-home exams. Their respective contributions to the final grade are listed below.
| Quizzes | (10%) | During recitations | Best ten (10) quizzes out of thirteen (13) used in computing this contribution to your grade | |
| Exam 1 | (25%) | In early October 2022 | Take-home exam | Answer Key will be available here |
| Released on 10/06/2022 | Coverage: Lecture Notes (Chapters 1 -- ), Homeworks # 1 -- , Quizzes # 1 -- | |||
| Exam 2 | (25%) | In early November 2022 | Take-home exam | Answer key was emailed |
| Released on 11/07/2022 | Coverage: Lecture Notes (Chapters 1 -- ), Homeworks # 1 -- , Quizzes # 1 -- | |||
| Final Exam | (40%) | Last day of class | Take-home exam | Answer key was emailed |
| Released online on 12/13/2022 | Coverage: |
| 08/29/2022 | First day of classes for Fall 2017 | |
| 08/30/2022 | First ENEE 620 class | Welcome to ENEE 620 |
| 09/05/2022 | Labor Day | Campus is closed. Last swim of the 2022 summer season! |
| 09/27/2022 | | Lecture is replaced by a joint recitation session (with Quizz # 4)
| |
| 09/29/2022 or 09/30/2022 | | Recitation session is replaced by the lecture cancelled on 09/27
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| 10/06/2022 | Test # 1 posted | Take-home exam -- Due 10/11/2022 | 11/01/2022 | Test # 2 posted | Take-home exam -- Due 11/15/2022 |
| 11/23/2022 | Thanksgiving | Campus is closed |
| 11/24/2022 | Thanksgiving | Campus is closed -- The turkey is carved and no recitation! |
| 12/08/2022 | Last day of class for ENEE 620 class | |
| 12/12/2022 | Last day of classes for Fall 2022 | |
| 12/13/2022 | Final Exam | Take-home exam -- Due 12/20/2022 |