About the course

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 257 or MATH 416.

Detailed course description, including course goals and instructional objectives.

Course information in course explorer


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LECTURES for sections ON1, ONL, X

Most lectures will be synchronous at 2-2.50pm CDT, MTWRF online via Zoom (link is in Canvas), but some will be pre-recorded.

All lectures will be recorded and available in the course's Mediaspace channel.

Lecture attendance is not required but is is strongly recommended in order for you to learn the course material well and obtain a good grade in the course.

Communication: It is the student's responsibility to attend lectures or watch the lecture recordings, as well as check their email daily, in case there are announcements from course staff. Missing a lecture and/or not checking your email will not excuse complying with course deadlines and policies.


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COURSE MATERIALS


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DISCUSSION

Active participation in your learning environment is vital to your success in this course.

Campuswire: For discussions and questions regarding course material. Code to join: 5632.

Student online behavior: In any social interaction, certain rules of etiquette are expected and contribute to more enjoyable and productive communication. The following are tips for interacting online via e-mail or discussion board messages, adapted from guidelines originally compiled by Chuq Von Rospach and Gene Spafford (1995):


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GRADING POLICIES

You can check your grades in Canvas

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:


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HOMEWORK ASSIGNMENTS

Homework assignment policy:

DRES: Students with documented disabilities must notify the instructor by June 16.


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QUIZZES AND EXAM INFORMATION

There will be weekly quizzes on Wednesdays and there will be a final exam on Friday, August 4.

You will have the option of taking the quizzes during lecture time, 2pm CDT, or at 8pm CDT, but you have to make a decision by the end of the first week of lectures (June 16). Please complete this form to indicate your preference (if you do not complete the form, we will assume you will take the quizzes at 2pm).

Your worst quiz grade will be dropped in order to account for sickness, travel, etc.

Quiz and exam dates:

  1. Quiz 1: June 21, 2pm CDT, or at 8pm CDT.
    Coverage: Chapter 1
     
  2. Quiz 2: June 28, 2pm CDT, or at 8pm CDT.
    Coverage: mainly topics listed in HWs 2 and 3.
     
  3. Quiz 3: July 5, 2pm CDT, or at 8pm CDT.
    Coverage: mainly topics listed in HWs 4 and 5.
     
  4. Quiz 4: July 12, 2pm CDT, or at 8pm CDT.
    Coverage: mainly topics listed in HWs 6 and 7.
     
  5. Quiz 5: July 19, 2pm CDT, or at 8pm CDT.
    Coverage: mainly topics listed in HWs 8 and 9.
     
  6. Quiz 6: July 26, 2pm CDT, or at 8pm CDT.
    Coverage: mainly topics listed in HW 10 and 11.
     
  7. Quiz 7: August 2, 2pm CDT, or at 8pm CDT.
    Coverage: mainly topics listed in HW 12 and 13.
     
  8. Final Exam: Friday, August 4.
    Coverage: topics listed in HWs 1-14.

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

If you miss a quiz, 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 quiz 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 extended 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. An unexcused absence from a quiz 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 16.







Online quiz/exam instructions:


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OFFICE HOURS

Summary of office hours times, from June 13 to August 3, except June 19 and July 4.

Zoom link for all office hours is in Canvas.

Hours Monday
except June 19		 Tuesday
except July 4		 Wednesday Thursday Friday
11-12pm Zoom Zoom Zoom Zoom Zoom
6-7pm Zoom Zoom Zoom Zoom Zoom
7-8pm Zoom Zoom Zoom Zoom Zoom
8-9pm Zoom Zoom Zoom Zoom


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COURSE STAFF

Instructor:

TA's:

Communication: It is the student's responsibility to attend lectures or watch the recordings, as well as check their email daily, in case there are announcements from course staff. Missing a lecture and/or not checking your email will not excuse complying with course deadlines and policies.

Please post your questions on the discussion board, Campuswire, instead of emailing the instructors or TAs directly because it is very likely that you're not the only one of enrolled in the course that has that same question. This way, others can take advantage of the responses to your questions, and other students might be able to assist you sooner.


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TOPICS

It is strongly recommended to read the notes before each lecture. The slides indicate the section order.

Concept constellation

Content from notes:


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TENTATIVE COURSE SCHEDULE

You will be expected to read the course notes in preparation for lectures. The table below indicates the tentative schedule for the topics.

Monday Tuesday Wednesday Thursday Friday
June 12
1.1 Embracing uncertainty
1.2 Axioms of probability
June 13
1.2 Axioms of probability
June 14
1.3 Calculating the size of various sets
June 15
1.3 Calculating the size of various sets
1.4 Probability experiments with equally likely outcomes
June 16
1.4 Probability experiments with equally likely outcomes
2.1 Random variables and probability mass functions
June 19

Juneteenth
NO CLASS
June 20
2.1 Random variables and probability mass functions
Jan 21

QUIZ
June 22
2.2 The mean and variance of a random variable
June 23
2.3 Conditional probabilities
2.4 Independence and the binomial distribution
June 26
2.4.1 Mutually independent events
2.4.2 Independent random variables (of discrete-type)
2.4.3 Bernoulli distribution
2.4.4 Binomial distribution
June 27
2.5 Geometric distribution
2.6 Negative binomial distribution (only)
June 28

QUIZ
June 29
2.7 The Poisson distribution
2.8 Maximum likelihood parameter estimation
2.10 The law of total probability, and Bayes formula
June 30
2.11 Binary hypothesis testing with discrete-type observations
2.11.1 Maximum likelihood (ML) decision rule
2.11.2 Maximum a posteriori probability (MAP) decision rule
July 3
2.11 Binary hypothesis testing with discrete-type observations
2.11.1 Maximum likelihood (ML) decision rule
2.11.2 Maximum a posteriori probability (MAP) decision rule
July 4

Independence day
NO CLASS
July 5

QUIZ
July 6
2.12 Reliability
2.12.1 Union bound
2.12.2 Network outage probability
July 7
2.12.3 Distribution of the capacity of a flow network
2.12.5 Reliability of a single backup
3.1 Cumulative distribution functions
July 10
3.1 Cumulative distribution functions
3.2 Continuous-type random variables
July 11
3.2 Continuous-type random variables
3.4 Exponential distribution
3.3 Uniform distribution
3.6 Linear scaling of pdfs and the Gaussian distribution
3.6.1 Scaling rule for pdfs
July 12

QUIZ
July 13
3.6.2 The Gaussian (normal) distribution
3.6.3 The central limit theorem and the Gaussian approximation
July 14
3.7 ML parameter estimation for continuous-type variables
3.10 Binary hypothesis testing with continuous-type observations
July 17
3.8 Functions of a random variable
3.8.1 The distribution of a function of a random variable
July 18
3.8.1 The distribution of a function of a random variable
3.8.2 Generating a random variable with a specified distribution
July 19

QUIZ
July 20
4.3 Joint probability density functions
July 21
4.3 Joint probability density functions
4.2 Joint probability mass functions
July 24
4.4 Independence of random variables
4.4.1 Definition of independence for two random variables
4.4.2 Determining from a pdf whether independence holds
July 25
4.5 Distribution of sums of random variables
4.5.1 Sums of integer-valued random variables
4.5.2 Sums of jointly continuous-type random variables
4.6 Additional examples using joint distributions
July 26

QUIZ
July 27
4.6 Additional examples using joint distributions
4.8 Correlation and covariance
July 28
4.9 Minimum mean square error estimation
4.9.1 Constant estimators
4.9.3 Linear estimators
4.9.2 Unconstrained estimators
July 31
4.9 Minimum mean square error estimation
4.9.1 Constant estimators
4.9.3 Linear estimators
4.9.2 Unconstrained estimators
August 1
4.10 Law of large numbers and central limit theorem
4.10.1 Law of large numbers
4.10.2 Central limit theorem
4.11 Joint Gaussian distribution
4.11.1 From the standard 2-d normal to the general
4.11.2 Key properties of the bivariate normal distribution
August 2

QUIZ
August 3

Reading day
NO CLASS
August 4

Final exam day
NO CLASS


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ADDITIONAL RESOURCES






COVID

There will recordings that will be available for students with excused absences. If you have an excused absence or you are feeling sick, please contact Prof. Alvarez at least one hour before the lecture you will miss. If it is due to an excused absence, please also provide the corresponding documentation.

Here are the Univeristy's policies if you test positive for COVID.

Here is the information for quarantine and isolation.






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.






Inclusivity

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.






Disability Resources and Educational Services (DRES)

Students with documented disabilities must notify the instructor within the first 7 days of classes.

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 disability@illinois.edu 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.






FERPA

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.






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.






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 the Student 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.






Run, hide, fight.

Emergencies can happen anywhere and at any time. It is important that we take a minute to prepare for a situation in which our safety or even our lives could depend on our ability to react quickly. When we’re faced with almost any kind of emergency – like severe weather or if someone is trying to hurt you – we have three options: Run, hide or fight.

Run, hide, fight video.

Run
Leaving the area quickly is the best option if it is safe to do so.
  • Take time now to learn the different ways to leave your building.
  • Leave personal items behind.
  • Assist those who need help, but consider whether doing so puts yourself at risk.
  • Alert authorities of the emergency when it is safe to do so.
Hide
When you can’t or don’t want to run, take shelter indoors.
  • Take time now to learn different ways to seek shelter in your building.
  • If severe weather is imminent, go to the nearest indoor storm refuge area.
  • If someone is trying to hurt you and you can’t evacuate, get to a place where you can’t be seen, lock or barricade your area if possible, silence your phone, don’t make any noise and don’t come out until you receive an Illini-Alert indicating it is safe to do so.
Fight
As a last resort, you may need to fight to increase your chances of survival.
  • Think about what kind of common items are in your area which you can use to defend yourself.
  • Team up with others to fight if the situation allows.
  • Mentally prepare yourself – you may be in a fight for your life

Please be aware of people with disabilities who may need additional assistance in emergency situations

Other resources