ECE 313/MATH 362

PROBABILITY WITH ENGINEERING APPLICATIONS

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

Text : ECE 313 Course Notes (hardcopy sold through ECE Stores, pdf file available.) Corrections to notes.
Optional Reading: D. V. Sarwate, Probability with Engineering Applications, Powerpoint Slides for ECE 313, Fall 2000.
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OFFICE HOURS

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

STAFF

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)

TOPIC SCHEDULE

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.

EXAM INFORMATION

Exam I:
- Thursday, July 1, 7-7.50pm CDT, via CBTF Online.
- The topics covered in Exam 1 are exactly the ones in the course notes up until (and including) section 2.5 (except for Section 1.5), as well as Section 2.10.

Exam II:

Thursday, July 15, 7-7.50pm CDT, via CBTF Online
The topics covered Exam 2 are exactly the ones in the course notes up until (and including) section 3.4, except for Sections 1.5 and 2.9 (those will not be included), with emphasis on the topics not covered in Exam I.

exam and its solution.

conflict exam and its solution.

Exam III:

Thursday, July 29, 7-7.50pm CDT, via CBTF Online.
The topics covered Exam 3 are exactly the ones in the course notes up until (and including) section 4.1, except for Sections 1.5, 2.9, 3.8.3 and 3.9 (those will not be included), with emphasis on the topics not covered in Exams I and II.

exam and its solution.

Conflict exam and its solution.

Final Exam:

Saturday, August 7, 10.30am-12.30pm (CDT), via CBTF Online.
The topics covered in the exam are exactly the ones in the course notes up until (and including) section 4.9, except for Sections 1.5, 2.9, 3.8.3, 3.9 and 4.7 (those will not be included), with emphasis on the topics not covered in Exams I, II and III.

exam and its solution.

conflict exam and its solution.

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:

Exam duration: The final exams will be 2 hours long, including scan/upload time, so we strongly advise you to finish your exam with plenty of time to spare, in case you run into issues scanning/uploading. We will deduct points of your grade per late minute after those first 50 minutes.

No collaboration allowed: You are not allowed to share or collaborate on this exam and all work should be your own; otherwise, an Academic Integrity report will be filed against you and sanctions will be applied.

Allowed materials: you may use one two-sided cheat sheet, but not the course notes nor slides nor review notes; otherwise, an Academic Integrity report will be filed against you and sanctions will be applied.

Calculations: Calculators and other electronic ways to do calculations, like Wolfram alpha, are not allowed and neither is searching online; otherwise, an Academic Integrity report will be filed against you and sanctions will be applied.

Solving the exam: you must solve the exam on blank sheets of paper. Tablets are not allowed for writing and you may not print the exam; otherwise, an Academic Integrity report will be filed against you and sanctions will be applied.
You must include ALL your work in your upload to get credit and to avoid an Academic Integrity report being filed against you and sanctions being applied.

An Academic Integrity report will be filed against you and sanctions will be applied for unauthorized actions.

Solution uploads: Make sure that your scans are legible and that you correctly assign each solution to its question, or you will be deducted at least 5% of the corresponding problem part.
- Instructions for uploading your solutions to Gradescope can be found here. Make sure you know how to do this before the exam so you don't waste time trying to figure out how to do it during the exam and lose points for lateness.
- Students reported issues with some free scanning apps, so below we have instructions for scanning with two different free apps that work very well.
- Instructions on how to scan the pdf of the solutions in Android are here.
- Instructions on how to scan the pdf of the solutions in MacOS are here.
- You MUST remain in the proctoring session until you are finished uploading, even if the proctor says you can leave before that. We will not accept your exam if you leave the proctoring session before finishing your submission to Gradescope, and you will get a zero in the exam.
- There is no need to email yourself the pdf of your solutions, you can upload directly from your phone, so try it out before the exam to save time.
- We set up an exam test run in Gradescope so you can practice scanning/uploading before the first exam. Successful submission of the exam test run before June 29 will provide a 1% extra credit on your overall course grade.

Proctoring: This course uses the College of Engineering Computer-Based Testing Facility service CBTF Online for its exams.
- Review our exam policies (above) and all policies on the CBTF website before June 29 so you can complete a Compass2g quiz regarding exam policies. Successful completion of the quiz before June 29 will account for a 1% extra credit on your overall course grade.
- Any violation/disregard of CBTF policy, like incorrect camera positioning, ignoring proctor's instructions, etc. may result in your exam not being accepted (giving a zero) or in an Academic Integrity report being filed against you with sanctions applied, depending on the situation.

Academic Integrity

Division of Rehabilitation-Education Services (DRES)

cbtf@illinois.edu

and

GRADING POLICIES

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.

15% Quizzes (PrairieLearn, your worst quiz will be dropped)
57% Hour exams (3 @ 19% each)
28% Final Examination

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

objective criteria (85% = A, 70% = B, 55% = C, etc.),

and

statistical criteria (above-average scores = B or better, etc.).

As a rough guideline, we intend to award

A's to scores greater than min(m+s,85)
B's to scores in the range min(m,70) to min(m+s,85),
C's to scores in the range min(m-s,55) to min(m,70)
D's to scores in the range max(m-2s,45) to min(m-s,55)
F's to scores below max(m-2s,45)

+ 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:

The reason for saying rough guideline is that we reserve the right to make minor adjustments (upwards or downwards) to each cut-off if we can find a significant gap in scores. However, the enrollment is large enough that significant gaps in scores are unlikely. After determining a cutoff we examine the final exam papers of students just below each cutoff to check for accuracy in grading. In effect, the exams are pre regraded. We do not artificially create gaps in the scores, so around 5-10% of students will still have scores just below a cutoff. After the scores and grades are posted, we will not increase a grade just because it is just below a cutoff. If we were to lower a cutoff for one student then another student would be just below the new cutoff, etc. Whatever we do, there will be students just below the actual cutoffs.
Regardless of your exam performance and the settings of the cut-offs, however, you will receive the same grade as everyone who has the same total score as you, and nobody who has a lower total score will receive a higher grade than you.

You can find the campus' Academic integrity policy here.

Quizzes

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.

Additional resources

Drop Deadlines Summer 2021
Academic integrity
Inclusivity
Disability Resources and Educational Services (DRES)
FERPA
Sexual misconduct
Support Resources and Supporting Fellow Students in Distress
Other campus resources

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.

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.

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.

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.

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.

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.

ECE 313/MATH 362 PROBABILITY WITH ENGINEERING APPLICATIONS Summer 2021