ECES 521: Probability and Random Variables

Fall AY 2013-2014

Instructor: John MacLaren Walsh, Ph.D. Office Hours: Thursday & Friday 10:00AM – 11:00AM. Office: Bossone 203. Office Phone: 215-895-2360. Email: jwalsh@ece.drexel.edu include ECES521 in the subject line of all course related emails.

Teaching Assistant: Yunshu Liu. Office Hours: Tuesday 1pm–3pm and by appointment. Office: Bossone 604. Email: yunshu6@gmail.com.

Wednesdays from 6:00PM-8:50PM in Randell Hall 327.

The course has a website http://www.ece.drexel.edu/walsh/eces521/eces521.html. You will need to check it periodically to obtain homework assignments throughout the quarter. We will attempt to also use the BBLearn system to deliver information regarding the course, including homework and exam grades as they are calculated, as well as the same information posted at the website above. However, emails should not be sent through this system, but rather directly to the instructor/TA at the email address above.

There will be three midterm exams during the second half of lecture. The exams will each be cumulative, and consist of problems to be solved that are similar to or extensions of homework problems. The exams will be closed book and closed notes. You may bring one 8.5 × 11 inch page with notes on the front and the back to the exam. This must be prepared entirely by you, and sharing these sheets are grounds for failure of the exam. The note sheet must be submitted along with the exam. Exams may not be rescheduled.

Homework should be neat and legible. Homework should be stapled before arriving at class, the first page should contain your name, and the order of the work should follow the order of problems as assigned. Number the problems clearly, and indicate the final answer clearly.

There will be three midterm exams, a final exam, all cumulative, and nine homeworks. The lowest midterm exam grade will be dropped. The homework will be graded, with some problems inspected only for completeness, while other problems inspected in detail. The lowest two homework grades will be dropped. The final grade score will consist of 20% homework (best seven of nine), 30% in class exams (best two of three) 50%, final exam 30%.

The course letter grade will be assigned based on the final numerical grade via the following table.

95 | 100 | A |

90 | 94 | A- |

87 | 89 | B+ |

83 | 86 | B |

80 | 82 | B- |

77 | 79 | C+ |

73 | 76 | C |

70 | 72 | C- |

65 | 69 | D+ |

60 | 64 | D |

0 | 59 | F |

At my discretion, I may curve course grades up (but not down). When I do curve, I assign the highest cluster of
grades A, the next highest cluster B, and then C or lower for the remainder. It is impossible for me to answer the
question ‘what grade will I get” at the week 6 withdraw deadline (11/2), please do not ask me this.

The following text is required for all students participating in the course.

- Introduction to Probability, 2nd E.d, Dimitri P. Bertsekas and John N. Tsitsiklis. Athena Scientific, Belmont, Massachusetts. ISBN 978-1-886529-23-6.

Other excellent reference texts, which are not required, but may be helpful as reading alternatives include:

- Probability, Random Variables, and Stochastic Processes, 4th Ed., A. Papoulis, McGraw-Hill. ISBN 978-0071226615.
- Probability and Probabilistic Reasoning for Electrical Engineering, T. L. Fine, Pearson Prentice Hall. ISBN 9780130205919.
- Probability, Statistics, and Random Processes for Electrical Engineering, A. Leon-Garcia, Pearson Prentice Hall. ISBN 978-0131471221.

Probability concepts. Single and multiple random variables. Functions of random variables. Moments and characteristic functions. Random number and hypothesis testing. Maximum likelihood estimation.

- Understanding of probabilistic models, conditional probability, total probability theorem, Bayes’ rule, and independence.
- Understanding of discrete random variables including probability mass functions, functions of random variables, expectation and variance, and multiple random variables.
- Understanding of continuous random variables including probability density functions, cumulative distribution functions, and normal random variables.
- Understanding of derived distributions, covariance and correlation, conditional expectation and variance, and sums of random variables.

Day | Date | Lecture | Book | Exam | Due | Assigned |

Wed | 9/25 | Lecture 1 | §1.1–1.7 | HW 1 | ||

Wed | 10/2 | Lecture 2 | § | Exam 1 | HW 1 | HW 2 |

Sun | 10/6 | Add/Drop Deadline | ||||

Wed | 10/9 | Lecture 3 | §2.1 – 2.4 | HW 2 | HW 3 | |

Wed | 10/16 | Lecture 4 | §2.5 – 2.8 | HW 3 | HW 4 | |

Wed | 10/23 | Lecture 5 | Exam 2 | HW 4 | HW 5 | |

Wed | 10/30 | Lecture 6 | §3.1 – 3.3 | HW 5 | HW 6 | |

Wed | 11/6 | Lecture 7 | §3.4 – 3.7 | HW 6 | HW 7 | |

Fri | 11/8 | Withdraw Deadline | ||||

Wed | 11/13 | Lecture 8 | §4.1 – 4.3 | Exam 3 | HW 7 | HW 8 |

Wed | 11/20 | Lecture 9 | §4.4 – 4.6 | HW 8 | HW 9 | |

Wed | 11/27 | Thanksgiving Break | ||||

Wed | 12/4 | Lecture 10 | HW 9 | |||

Wed | 12/11 | Final Exam |

- September 25: Lecture 1
- HW 1 assigned.

- October 2: Lecture 2.
- October 9: Lecture 3
- October 16: Lecture 4
- October 23: Lecture 5
- October 30: Lecture 6
- November 6: Lecture 7
- November 13: Lecture 8
- November 20: Lecture 9
- November 27: Thanksgiving Break – No Lecture.
- December 4: Lecture 10
- HW 9 due at the beginning of class (6:00PM)

- December 11: Final Exam (Cumulative)
- You may bring two sides of a 8.5 by 11 inch piece of paper, handwritten to the exam. You must prepare this sheet yourself, and you will turn it in with your final exam.
- A practice final exam is available here.