ECE 313/MATH 362
PROBABILITY WITH ENGINEERING APPLICATIONS
|Section||Meeting time and place||Instructor|
|ONL and ON1||10 MTWRF - Zoom live lectures
Zoom password is in Compass
e-mail: alvarez AT illinois dot edu
ECE 313 (also cross-listed as MATH 362) is a 3-credit undergraduate course on probability theory and statistics with applications to engineering problems primarily chosen from the areas of communications, control, signal processing, and computer engineering.
EE and CompE students must complete one of the two courses ECE 313 or Stat 410.
Prerequisite : Math 286 or Math 415
Detailed course description, including course goals and instructional objectives.
Course information in course explorer
except July 3
except July 4
|8-9am||Der-Han Huang||Victor Shangguan|
|6-7pm||Der-Han Huang||Victor Shangguan||Ali Yekkehkhany|
|9-10pm||Juan Alvarez||Juan Alvarez|
Instructor: Juan Alvarez (alvarez AT illinois dot edu)
|Ali Yekkehkhany (yekkehk2 AT illinois dot edu)|
|Victor Shangguan (xs27 AT illinois dot edu)|
|Der-Han Huang (dhhuang2 AT illinois dot edu)|
It is strongly recommended to read the notes before each lecture.
See Quizzes for quiz information.
|Quiz #||Quiz deadline
|Concepts (Notes sections)[Short videos]||Short Answer Questions (SAQ) and Problems from course notes to prepare for Quizzes|
* How to specify a set of outcomes, events, and probabilities for a given experiment (Ch 1.2)
* Set theory (e.g. de Morgan's law, Karnaugh maps for two sets) (Ch 1.2)
* Using Karnaugh maps for three sets (Ch 1.4)[Karnaughpuzzle, SAQ1.2]
* Using principles of counting and over counting; binomial coefficients (Ch 1.3-1.4) [ILLINI, SAQ 1.3, SAQ 1.4, PokerIntro, PokerFH2P]
- Skip Section 1.5 completely, and Sections 2.1-2.2 temporarily.
* Conditional probability (Ch 2.3) [team selection][SAQ 2.3]
* SAQs for Sections 1.2, 1.3, 1.4, 2.3.
* Problems 1.2, 1.4, 1.6, 1.8, 1.10, 1.12, 2.4, 2.12, 2.16 .
Optional: [SAQ 1.5]
* independence of events (Ch 2.4.1)[SimdocIntro][Simdoc-Minhash1]
- Skip Sections 2.4.2-2.9 temporarily.
* law of total probability (Ch 2.10) [deuce] [SAQ 2.10]
* Bayes formula (Ch. 2.10)
* random variables and probability mass functions (Ch 2.1) [pmfmean]
|* SAQs for Section 2.10
* Problems 2.2 (only pmf), 2.6 (a,c), 2.14, 2.32, 2.34.
*mean of a function of a random variable (LOTUS) (Ch 2.2)
* scaling of expectation, variance, and standard deviation (Ch 2.2) [SAQ 2.2]
- Already went through Sections 2.3-2.4.1.
* independence of random variables and Bernoulli distribution (Ch 2.4.2-2.4.3)[SimdocIntro][Simdoc-Minhash1]
Exam 1: Wednesday, July 1.
|* SAQs for Section 2.2.
* Problems 2.2, 2.6, 2.8, 2.10.
* binomial distribution (how it arises, mean, variance, mode) (Ch 2.4.3-2.4.4)[SAQ 2.4][bestofseven]
* geometric distribution (how it arises, mean, variance, memoryless property) (Ch. 2.5)[SAQ 2.5]
* Bernoulli process (definition, connection to binomial and geometric distributions) (Ch 2.6)[SAQ 2.6]
NO lecture on Friday, July 3.
|* SAQs for Sections 2.4, 2.5, 2.6 (1,2).
* Problems 2.18, 2.20, 2.22, 2.24.
* Poisson distribution (how it arises, mean, variance) (Ch 2.7)[SAQ 2.7]
- Skip Section 2.8 temporarily and Section 2.9 completely. Already went through Section 2.10.
* Hypothesis testing -- probability of false alarm and probability of miss (Ch. 2.11)
* ML decision rule and likelihood ratio tests (Ch 2.11) [SAQ 2.11]
* MAP decision rules (Ch 2.11)
|* SAQs for Sections 2.6, 2.7, 2.11
* Problems 2.30(a), 2.36, 2.40.
* Maximum likelihood parameter estimation (definition, how to calculate for continuous and discrete parameters) (Ch 2.8)[SAQ 2.8][hypergeometric]
- Skip Section 2.9 completely. Already went through Sections 2.10-2.11.
* union bound (Ch 2.12.1) [SAQ 2.12]
* network outage probability and distribution of capacity (Ch 2.12.2-2.12.3)
- Skip Subsections 2.12.4-2.12.5 completely.
Exam 2: Wednesday, July 15.
* SAQs for Sections 2.8, 2.12
* Problems 2.26, 2.30(c), 2.42, 2.44, 2.46
* cumulative distribution functions (Ch 3.1)[SAQ 3.1]
* probability density functions (Ch 3.2) [SAQ 3.2] [simplepdf]
* SAQs for Sections 3.1-3.2.
* Problems 3.2, 3.4, 3.6, 3.8.
* uniform distribution (Ch 3.3)
* exponential distribution (Ch 3.4) [SAQ 3.4]
* Poisson processes (Ch 3.5) [SAQ 3.5]
|* SAQs for Sections 3.3-3.5.
* Problems 3.10, 3.12 and 3.14.
* scaling rule for pdfs (Ch. 3.6.1)[SAQ 3.6]
* Gaussian (normal) distribution (e.g. using Q and Phi functions) (Ch. 3.6.2) [SAQ 3.6] [matlab help including Qfunction.m]
* the central limit theorem and Gaussian approximation (Ch. 3.6.3) [SAQ 3.6]
* ML parameter estimation for continuous type random variables (Ch. 3.7)[SAQ 3.7]
- Skip Sections 3.8 temporarliy and section 3.9 completely.
* binary hypothesis testing for continuous type random variables (Ch 3.10) [SAQ 3.10]
|* SAQs for Section 3.6, 3.7, and 3.10.
* Problems 3.16, 3.18(c), 3.20, 3.22 and 3.24.
* the distribution of a function of a random variable (Ch 3.8.1)[SAQ 3.8]
Exam 3: Wednesday, July 29.
|* SAQs for Sections 3.8.1.
* Problems 3.26, 3.28, 3.30, 3.32(a-b), 3.38(a-b).
* generating random variables with a specified distribution (Ch 3.8.2)
- Skip Sections 3.8.3 and 3.9 completely.
* joint CDFs (Ch 4.1)[SAQ 4.1]
- Skip Section 4.2 temporarily.
* joint pdfs (Ch 4.3)[SAQ 4.3]
|* SAQs for Sections 3.8.2, 4.1, 4.3.
* Problems 3.32(c), 4.2(a-c), 4.6, 4.10(b-e).
* joint pmfs (Ch 4.2)[SAQ 4.2]
* joint pdfs of independent random variables (Ch 4.4)[SAQ 4.4]
* distribution of sums of random variables (Ch 4.5)[SAQ 4.5]
|* SAQs for Sections 4.2, 4.4-4.5.
* Problems 4.2(d), 4.4, 4.8, 4.10(a), 4.12, 4.14.
* more problems involving joint densities (Ch 4.6)[SAQ 4.6.]
- Skip Section 4.7.
* correlation and covariance (e.g. scaling properties) (Ch 4.8)[SAQ 4.8]
* minimum mean square error linear estimator (Ch 4.9.3)[SAQ 4.9]
* minimum mean square error unconstrained estimators (Ch 4.9.2)
Final exam: Saturday, August 8.
|* SAQs for Sections 4.6, 4.8-4.9
* Problems 4.16, 4.18, 4.20, 4.22, 4.24, 4.26, 4.28.
Instructions regarding what is allowed on the exam, as well as the Gradescope procedure to download the exam and upload the solutions can be found here
Instructions for the exam proctoring are posted on the CBTF Online website. You will need two internet connected devices, one that can be positioned to use its video feed to proctor, and another to have access to the exam.
Read both sets of instructions before the exam, in case you have any questions, and also so you know how to sign up for CBTF proctoring.
Old exams: You can find copies of old exams here.
Regrades: We use Gradescope to grade the exams, so instead of receiving a hard copy of your exam in class, you will receive an email from Gradescope so you can log in and see your graded exam. If after looking at the posted solutions, you feel there was an inaccuracy in the grading of your exam, you can request a regrade within Gradescope itself. An email with a deadline for the regrades will be sent out once the exams are graded.
If you miss a midterm exam, the following procedures apply: To receive an excused absence, you must either arrange your absence in advance with your instructor (i.e., prior to the absence), or complete an Excused Absence Form at the Undergraduate College Office, Room 207 Engineering Hall, indicating that you missed the midterm exam and the reason for the absence. This form must be signed by a physician or medical official for a medical excuse, or by the Office of the Dean of Students (Emergency Dean, 610 E. John Street, 3330050) for a personal excuse due to personal illness, family emergencies, or other uncontrollable circumstances. Present the completed form in person to your section instructor as soon as possible after you return. Scores on midterms due to excused absences will not be made up. Your midterm score for an excused absence will be the weighted average of the other midterm score and final exam score. An unexcused absence from a midterm will be counted as a 0.
If for some reason of emergency such as severe illness you are not able to take the final exam at the required time, you will need to obtain a written excuse from the Office of the Dean of Students.
DRES: Students with documented disabilities must notify the instructor by June 19.
You can find the campus' Academic integrity policy here.
Throughout the Summer, you will take 13 quizzes via PrairieLearn. Only the highest 11 out of your 13 quiz scores will be factored into your course grade.
In addition, Quiz 0 is offered as a practice quiz, with no course credit. It shows how PrarieLearn quizzes work, and it reviews a couple of topics that come up in the course. It also has some notes to keep in mind during other quizzes, regarding multi-part questions and multi-attempt questions.
Deadline: The deadline to take each quiz is midnight of the day indicated in the course schedule. Any parts of a quiz that are not finished by the corresponding deadline will get zero credit. You will have 20 minutes to complete each quiz.
We recommend you read the notes and work out the listed problems before taking the quizzes. The questions on the quizzes are very similar to the short answer questions and even numbered problems in the course notes, as identified on the concept matrix on the main website page for the course. Typically a quiz will have two questions with multiple parts. They could be multiple choice, checkbox (select multiple options from a list), or short answer with answers being an integer, a fraction, or a number in decimal form that should be accurate to within two significant digits, or a symbolic expressions.
The questions for each quiz assigned to a particular student are selected at random from a list of possible questions, and the questions themselves may have random variations. Nevertheless, please refrain from discussing the quiz questions with other students until after the quiz period ends.
When you finish your quiz, you will see the correct answers and your score on the quiz. As you are reviewing your quiz at the end, please take a mental note and memorize any questions you have regarding the quiz as you will not have access to the quiz once are finished. After the quiz period has ended, you may come to office hours and ask specific questions regarding the quiz. You will need to bring specific questions about the quiz as the TAs and instructors will not open your quiz and go through it with you.
Tip: The quizzes test your knowledge of checkpoints on your road to learning how to solve problems for this course. You will be tested over the same material again on the midterms and final exams, without benefit of focusing on a fairly narrow list of problems. So to use your time most efficiently, read the assigned material in the notes, paying special attention to the examples. Attend and participate in class. Work out the assigned problems on your own, looking at the answers only if you are truly stuck. Start early in the week; don't wait until just before the quiz. If you work the problems yourself, you will be familiar enough with the problems to do well on the quizzes. And, more to the point, you will be in a great position for the exams, and for overall success in the course and beyond.
You can find the campus' Academic integrity policy here.
Access to PrairieLearn: If you enroll after the first day of classes, you might not have immediate access to PrairieLearn. Please email the intructor to give you access. This might take a few hours, so do not wait until just before the first deadline to notify the instructor.