ECE 313/MATH 362


Summer 2021

Slides --- Recorded lectures --- Jamboard --- Quizzes --- Office hours --- Exams --- Topic schedule --- Grading Policies --- Piazza --- Staff --- FAQ --- Additional resources

Section Meeting time and place Instructor
ONL and ON1 10-10.50am CST, MTWRF - Zoom live lectures
Zoom password is in Compass2G.
Juan Alvarez
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. Students taking ECE 313 might consider taking ECE 314, Probability Lab, at the same time.

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

back to top


Summary of office hours times and locations, from June 15 to August 5, except July 5.
Zoom password is in Compass.
Hours Monday
except July 5
Tuesday Wednesday Thursday Friday
8-9am Pulkit Katdare Pulkit Katdare Pulkit Katdare Pulkit Katdare Pulkit Katdare
11am-12pm Juan Alvarez Juan Alvarez Juan Alvarez Juan Alvarez Juan Alvarez
5-6pm Junyeob Lim Junyeob Lim Junyeob Lim Junyeob Lim Junyeob Lim
8-9pm Junyeob Lim Junyeob Lim Junyeob Lim Junyeob Lim Junyeob Lim

back to top


Instructor: Juan Alvarez (alvarez AT illinois dot edu)

Graduate Teaching Assistants:
Pulkit Katdare (katdare2 AT illinois dot edu)
Junyeob Lim (junyeob2 AT illinois dot edu)

back to top


It is strongly recommended to read the notes before each lecture.

See Quizzes for quiz information.

Quiz # Quiz deadline
(midnight CST)
Concepts (Notes sections)[Short videos] Short Answer Questions (SAQ) and Problems from course notes to prepare for Quizzes
0 Saturday,
June 19
Quiz 0 is a practice quiz and carries no course credit. It covers two topics that come up later in the course:
* The sum of a geometric series.
* The power series for exp(x).
* The chain rule for differentiation.
* Properties of logarithms
1 Tuesday,
June 22
* 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; probability experiments with equally likely outcomes (Ch 1.3-1.4) [ILLINI, SAQ 1.3, SAQ 1.4, PokerIntro, PokerFH2P]
- Skip Section 1.5 completely.
* SAQs for Sections 1.2, 1.3, 1.4.
* Problems 1.2, 1.4, 1.6, 1.8, 1.10, 1.12.
Optional: [SAQ 1.5]
2 Saturday,
June 26
* random variables and probability mass functions (Ch 2.1) [pmfmean]
* mean of a function of a random variable (LOTUS) (Ch 2.2) [pmfmean]
* scaling of expectation, variance, and standard deviation (Ch 2.2) [SAQ 2.2]
* Conditional probability (Ch 2.3) [team selection][SAQ 2.3]
* independence of events (Ch 2.4.1)[SimdocIntro][Simdoc-Minhash1]
* SAQs for Sections 2.2, 2.3.
* Problems 2.2, 2.4, 2.6, 2.8, 2.10, 2.12, 2.14, 2.16.
3 Thursday,
July 1

* independence of random variables and Bernoulli distribution (Ch 2.4.2-2.4.3)[SimdocIntro][Simdoc-Minhash1]
* 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]
- Skip Sections 2.6-2.9 temporarily.
* law of total probability (Ch 2.10) [deuce] [SAQ 2.10]
* Bayes formula (Ch. 2.10)

Exam 1: Thursday, July 1. NO lecture.
* SAQs for Sections 2.4, 2.5, 2.10.
* Problems 2.18, 2.20, 2.22, 2.24.
4 Tuesday,
July 6

* Bernoulli process (definition, connection to binomial and geometric distributions) (Ch 2.6)[SAQ 2.6]
* Poisson distribution (how it arises, mean, variance) (Ch 2.7)[SAQ 2.7]
* Maximum likelihood parameter estimation (definition, how to calculate for continuous and discrete parameters) (Ch 2.8) [SAQ 2.8][hypergeometric]
- Skip Section 2.9. Already went through Section 2.10.

NO lecture on Monday, July 5.
* SAQs for Sections 2.6, 2.7, 2.8.
* Problems 2.26, 2.30(a,c).
5 Saturday,
July 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)
* union bound (Ch 2.12.1) [SAQ 2.12]
* SAQs for Section 2.11.
* Problems 2.32, 2.34, 2.36, 2.40, 2.42.
6 Thursday,
July 15
* network outage probability, distribution of capacity and more applications of the union bound (Ch 2.12.2-2.12.4) [SAQ 2.12]
* cumulative distribution functions (Ch 3.1) [SAQ 3.1]
* probability density functions (Ch 3.2) [SAQ 3.2] [simplepdf]
* exponential distribution (Ch 3.4) [SAQ 3.4]
* uniform distribution (Ch 3.3) [SAQ 3.3]

Exam 2: Thursday, July 15. No lecture.
* SAQs for Sections 2.12, 3.1, 3.2, 3.3, 3.4.
* Problems 2.44, 2.46, 3.2, 3.4, 3.6, 3.8, 3.10.
7 Tuesday,
July 20
* Poisson processes (Ch 3.5) [SAQ 3.5]
* scaling rule for pdfs (Ch. 3.6.1) [SAQ 3.6]
* SAQs for Sections 3.5, 3.6.1.
* Problems 3.12, 3.14.
8 Saturday,
July 24
* 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 Sections 3.6(1,2), 3.7, 3.10.
* Problems 3.16, 3.18(c), 3.20, 3.22, 3.24.
9 Thursday,
July 29
* the distribution of a function of a random variable (Ch 3.8.1)[SAQ 3.8]
* generating random variables with a specified distribution (Ch 3.8.2) [SAQ 3.8]
- Skip Sections 3.8.3 and 3.9 completely.
* joint CDFs (Ch 4.1)

Exam 3: Thursday, July 29. No lecture.
* SAQs for Sections 3.8.
* Problems 3.26, 3.28, 3.30, 3.32, 3.38(a-b).
10 Tuesday,
August 3
* joint pdfs (Ch 4.3) [SAQ 4.3]
* 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, 4.3, 4.4, 4.5.
* Problems 4.2, 4.4, 4.6, 4.8, 4.10.
11 Friday,
August 6
* 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)[SAQ 4.9]

Final exam: Saturday, August 7, 10.30am-12.30pm (CDT)
* SAQs for Sections 4.6, 4.8, 4.9.
* Problems 4.12, 4.14, 4.16, 4.18, 4.20, 4.22, 4.24, 4.26, 4.28.

back to top


Old exams: You can find copies of old exams here.

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.

Exam instructions:

back to top


You can check your grades in Illinois Compass 2g

Grade Distribution Formula: Scores will be weighted as shown below to determine your total score, which in turn, will determine your grade.

Letter Grades: After computing each student's total score we find the mean m and the standard deviation s of the total scores. Letter grades are assigned using cut-offs that are based roughly on a mixture of and As a rough guideline, we intend to award + and - grades are typically awarded at the edges of the above cut-offs. The percentages of A's and B's awarded in ECE 313 are comparable to those awarded in 300-level required courses in the ECE Department.

Notes regarding grading practices:

You can find the campus' Academic integrity policy here.

back to top


Throughout the Summer, you will take 11 quizzes via PrairieLearn. Only the highest 10 out of your 11 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. In multi-part questions, you need to enter an answer for each part of the question for it to be graded. If you do not know the answer, enter a zero.

Deadline: The deadline to take each quiz is midnight (CST) 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 25 minutes to complete each quiz. Each quiz will open as soon as the previous one closes.

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 examples, 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 quizzes are meant to be solved once and get the correct answer. We used to have them paper based at the end of lectures, so there were no re-tries, you solved it and turned it in. In Prairielearn you get multiple tries in some cases, but those multiple tries are bonus opportunities for you. If you are attempting the problem multiple times, there is a good chance you won't have enough time.

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.

back to top

Additional resources

back to top
Academic integrity

The University of Illinois at Urbana-Champaign Student Code should is very important for you to know.

Students should pay particular attention to Article 1, Part 4: Academic Integrity. Academic dishonesty may result in a failing grade. Every student is expected to review and abide by the Academic Integrity Policy. Ignorance is not an excuse for any academic dishonesty. It is your responsibility to read this policy to avoid any misunderstanding. Do not hesitate to ask the instructor(s) if you are ever in doubt about what constitutes plagiarism, cheating, or any other breach of academic integrity.

back to top

The effectiveness of this course is dependent upon the creation of an encouraging and safe classroom environment. Exclusionary, offensive or harmful speech (such as racism, sexism, homophobia, transphobia, etc.) will not be tolerated and in some cases subject to University harassment procedures. We are all responsible for creating a positive and safe environment that allows all students equal respect and comfort. I expect each of you to help establish and maintain and environment where you and your peers can contribute without fear of ridicule or intolerant or offensive language.

back to top
Disability Resources and Educational Services (DRES)

To obtain disability-related academic adjustments and/or auxiliary aids, students with disabilities must contact the course instructor and the Disability Resources and Educational Services (DRES) as soon as possible.

To contact DRES, you may visit 1207 S. Oak St., Champaign, call 333-4603, e-mail or go to the DRES website.

If you are concerned you have a disability-related condition that is impacting your academic progress, there are academic screening appointments available on campus that can help diagnosis a previously undiagnosed disability by visiting the DRES website and selecting “Sign-Up for an Academic Screening” at the bottom of the page.

back to top

Any student who has suppressed their directory information pursuant to Family Educational Rights and Privacy Act (FERPA) should self-identify to the instructor to ensure protection of the privacy of their attendance in this course. Click here for more information on FERPA.

back to top
Sexual misconduct

The University of Illinois is committed to combating sexual misconduct. Faculty and staff members are required to report any instances of sexual misconduct to the University’s Title IX and Disability Office. In turn, an individual with the Title IX and Disability Office will provide information about rights and options, including accommodations, support services, the campus disciplinary process, and law enforcement options. A list of the designated University employees who, as counselors, confidential advisors, and medical professionals, do not have this reporting responsibility and can maintain confidentiality, can be found here. Other information about resources and reporting is available here.

back to top
Support Resources and Supporting Fellow Students in Distress

As members of the Illinois community, we each have a responsibility to express care and concern for one another. If you come across a classmate whose behavior concerns you, whether in regards to their well-being or yours, we encourage you to refer this behavior to the Student Assistance Center (1-217-333-0050) or online. Based upon your report, staff in the Student Assistance Center reaches out to students to make sure they have the support they need to be healthy and safe. Further, as a Community of Care, we want to support you in your overall wellness. We know that students sometimes face challenges that can impact academic performance (examples include mental health concerns, food insecurity, homelessness, personal emergencies). Should you find that you are managing such a challenge and that it is interfering with your coursework, you are encouraged to contact theStudent Assistance Center (SAC)in the Office of the Dean of Students for support and referrals to campus and/or community resources. The SAC has a Dean on Duty available to see students who walk in, call, or email the office during business hours. For mental health emergencies, you can call 911 or contact the Counseling Center.