ECE 313
Probability with Engineering Applications
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Section  Type  Times  Days  Location  Instructor 

B  DIS  1400  1450  M W F  3017 Electrical & Computer Eng Bldg  Olgica Milenkovic 
C  DIS  1000  1050  M W F  3015 Electrical & Computer Eng Bldg  Bruce Hajek 
D  DIS  1100  1150  M W F  3017 Electrical & Computer Eng Bldg  Venugopal Veeravalli 
E  DIS  1300  1350  M W F  3017 Electrical & Computer Eng Bldg  Pramod Viswanath 
X  DIS  0800  0920  T R  3013 Electrical & Computer Eng Bldg  Ravishankar Iyer 
Web Page  http://courses.engr.illinois.edu/ece313/ 

Official Description  Probability theory with applications to engineering problems such as the reliability of circuits and systems to statistical methods for hypothesis testing, decision making under uncertainty, and parameter estimation. Course Information: Same as MATH 362. Credit is not given for both ECE 313 and MATH 461. Prerequisite: ECE 210. 
Subject Area  Core Curriculum 
Course Prerequisites  Credit in ECE 210 
Course Directors 
Bruce Hajek

Detailed Description and Outline 
To develop an understanding of probabilistic phenomena in electronic systems with applications to reliability, system engineering, engineering decisionmaking, and parameter estimation. Topics:

Computer Usage 
No required assignments; optional assignments may be given. 
Topical Prerequisities 

Texts 
S. Ross, A First Course in Probability, 7th ed., Macmillan, 2005. 
ABET Category 
Engineering Science: 3 credits 
Course Goals 
ECE 313 is a juniorlevel 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 seniorlevel elective courses. The course serves as a prerequisite or corequisite for advanced undergraduatelevel technical electives in the areas of signal processing, computer networks, and communications such as
as well as numerous graduate courses. 
Instructional Objectives 
At the end of this course, the student will be able to apply the knowledge of probability and statistics gained in this course to several different types of problems in engineering. 1. Given a network of hosts that communicate with each other over links that are prone to failure, the student will be able to compute the probability that there exists a viable communication path between any two nodes in the network. (a, l, m, n) The student will also be able to model failure modes for systems composed of several subsystems as a network problem, and to solve such problems. (a, l, m, n) 2. The student will be able to formulate engineering decisionmaking problems as hypothesis testing schemes that compare likelihood ratios to thresholds. (a, c, e, l, m, n) The student will be able to calculate the thresholds required to meet design specifications such as maximum falsealarm probabilities or detection probabilities in radar decision problems. (a, b, l, m, n) The student will be able to design tests using Bayesian methods for the purpose of minimizing the average probability of error. (a, c, e, l, m, n) 3. The student will be able to specify maximumlikelihood estimates for system parameters. (a, b, c, e, l, m, n) The student will be able to estimate confidence intervals for parameters for any specified confidence level. (a, l , m, n) 4. The student will be able to compute probability distributions for the parameters of various systems, to estimate average values and variances of these parameters, and to estimate the probabilities that various design specifications are met. (a, b, l, m, n)
