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,
Section D: Ada Poon , CSL 129,
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,
TA office hours

Tuesdays1-3pm and Fridays 3-5pm in 330L Everitt Lab
Exceptions: final review session Friday Dec 7th 3-5p CSL 351

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 Bayes’ 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)