ECE 313 Probability with Engineering Applications | |
Objectives | ECE 313 is a junior-level required course in both the EE and CompE curricula. The course introduces students to the theory of probability and its applications to engineering problems in the reliability of circuits and systems, and to statistical methods for hypothesis testing, decisionmaking under uncertainty, and parameter estimation. The goal is to provide the student with an adequate knowledge of probability and probabilistic reasoning in engineering analyses, and of statistical methods to enable the student to apply these techniques in advanced senior-level elective courses. The course serves as a prerequisite or co-requisite for advanced undergraduate level technical electives in the areas of signal processing, computer networks, and communications such as ECE 418 - Image and Video Processing ECE 438 - Computer Communication Networks ECE 459 - Communication Systems ECE 463 - Digital Communications Laboratory as well as numerous graduate courses. |
Prerequisites | ECE 210 |
Credit | 3 hours |
Instructors | Section C:Tamer Basar, CSL 356, basarl@uiuc.edu Section D: Ada Poon , CSL 129, poon@uiuc.edu |
Class hours | Section C:MWF 10-10:50am in 106B3 Engineering Hall Section D: MWF 11-11:50am in 106B6 Engineering Hall |
Office hours | Mondays2-3pm in the office of the respective instructor |
TA | Xiaolan Zhang, xzhang29@uiuc.edu |
TA office hours | Tuesdays1-3pm and Fridays 3-5pm in 330L Everitt Lab |
Textbook | S. Ross, A First Course in Probability, 7th Ed., Prentice-Hall, 2006. |
References | C. Ash, Probability Tutoring Book, IEEE Press, 1992. Previous class websites |
Homeworks | Homeworks will be assigned on a weekly basis and posted on the course homepage on Wednesday. They will be due at the beginning of class on the following Wednesday. Late homeworks will not be accepted without prior permission. If you cannot attend class on the homework due date, you must make arrangements to have your homework turned in to the instructor before class. Homeworks will cover material including the Friday class of the week in which they are assigned. Homework grades are posted at COMPASS. Graded homeworks will be handed out in the class. Each homework is worth a maximum of 100 points that will be evenly distributed over all problems assigned for that homework. The lowest scored homework will be dropped in the total. |
Exams | There will be two mid-term exams and one final exam. For the mid-terms, a single 8 1/2 by 11 sheet of notes is permitted (you may use both sides); but otherwise the exams are closed book. Laptops, calculators, palm-pilots, tables of integrals etc. will neither be necessary nor be permitted. For the final exam, two 8 1/2 by 11 sheets of notes are permitted (you may again use both sides). The sheets can be hand-written, but the font size should not be too small, necessitating the use of a magnifying glass; as a general rule, any size smaller than the equivalent of a 10 pt font is not permitted. Schedules for the Exams: Mid-Term 1: October 8, 7-8:30 PM, 269 Everitt Lab. Mid-Term 2: November 12, 7-8:30 PM, 269 Everitt Lab. Final: December 10, 8:00-11:00 AM (room TBA) |
Grading | 10% homeworks, 50% mid-term, and 40% final exam |
Lecture | Date | Topics | Reading | Notes | Homework due |
1 | 08.22 | Introduction | 1.1-1.5 | info | |
2 | 08.24 | Probability model | 21.-2.3 | ||
3 | 08.27 | Axioms of probability I | 2.4-2.5 | ||
4 | 08.29 | Axioms of probability II | 2.6-2.7 | hw1, soln1 | |
5 | 08.31 | Axioms of probability III | 2.6-2.7 | ||
09.03 | Labor Day, no class | ||||
6 | 09.05 | Random variables | 4.1-4.3 | hw2, soln2 | |
7 | 09.07 | Mean, LOTUS, and variance | 4.4-4.5 | ||
8 | 09.10 | Independent trials | 4.6 | ||
9 | 09.12 | Statistical estimation | 4.6 | hw3, soln3 | |
10 | 09.14 | Confidence intervals | 8.1-8.2 | ||
11 | 09.17 | Important counting random variables | 4.7-4.8 | ||
12 | 09.19 | Conditional probability | 3.1-3.2 | hw4, soln4 | |
13 | 09.21 | Theorem of total probability | 3.3 | ||
14 | 09.24 | Bayesâ€™ formula | 3.3-3.5 | ||
15 | 09.26 | Decision-making under uncertainty I | dm | hw5, soln5 | |
16 | 09.28 | Decision-making under uncertainty II | |||
17 | 10.01 | Decision-making under uncertainty III | |||
18 | 10.03 | System reliability I | hw6, soln6 | ||
19 | 10.05 | System reliability II | |||
20 | 10.08 | Cumulative distribution function | 4.9 | ||
Midterm 1 (7-8:30 PM, 269 EL) | fall06, sp07 | midterm1, midterm1soln | |||
10.10 | No class after midterm | ||||
21 | 10.12 | Uniform and Exponential random variables | 5.3, 5.5 | ||
22 | 10.15 | Other continuous random variables | 5.6 | ||
23 | 10.17 | Expectation of continuous random variables | 5.2 | hw7, soln7 | |
24 | 10.19 | Expectation of functions of continuous random variables | 5.2-5.6 | ||
25 | 10.22 | Gaussian random variable | 5.4 | ||
26 | 10.24 | Poisson process | 9.1 | hw8, soln8 | |
27 | 10.26 | Functions of random variables I | 5.7 | ||
28 | 10.29 | Functions of random variables II | 5.7 | ||
29 | 10.31 | Hazard rates and system reliability | 5.5 | hw9, soln9 | |
30 | 11.02 | Decision-making under uncertainty IV | |||
31 | 11.05 | Joint distributions of random variables | 6.1 | ||
32 | 11.07 | Joint probability mass functions | 6.2, 6.4 | hw10, soln10 | |
33 | 11.09 | Joint continuous random variables I | 6.2, 6.3 | ||
34 | 11.12 | Joint continuous random variables II | 6.5 | ||
Midterm 2 (7-8:30 PM, 269 EL) | fall06, sp07 | midterm2, midterm2soln | |||
35 | 11.14 | Functions of many random variables I | 6.7 | ||
11.16 | No class | ||||
36 | 11.26 | Functions of many random variables II | |||
37 | 11.28 | Functions of many random variables III | hw11, soln11 | ||
38 | 11.30 | Expectation, covariance, and correlation | |||
39 | 12.03 | Jointly Gaussian random variables | |||
40 | 12.05 | Conditional probabilities | hw12, soln12 | ||
41 | 12.07 | Mean-square estimation | |||
12.10 | Final Exam (8-11 AM, 135 MEB) | fall06, sp07 | final, finalsoln | ||
12.11 | Conflict Final Exam (8-11 AM, 141 CSL) |