ECE 313/MATH 362

PROBABILITY WITH ENGINEERING APPLICATIONS

Summer 2022

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

• 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.
• Reserve Books

STAFF

Instructor: Juan Alvarez (alvarez AT illinois dot edu)

HOMEWORKS

• There will be 1-2 homeworks per week. Due dates are posted in Canvas.
• Homeworks will be posted and submitted made via Gradescope. You can join the course there with the entry code 6ZPVB5, use your U of I email (not a personal one) to register and use your UIN as your Student ID #.
  1. Instructions for uploading your solutions to Gradescope can be found here.
  2. Instructions on how to scan the pdf of the solutions in Android are here.
  3. Instructions on how to scan the pdf of the solutions in MacOS are here.
• Homeworks will be due by 7pm CDT. Late homeworks will receive a 2% grade reduction per minute.
• In order to account for sickness, travel, etc., your 2 lowest homework grades will be dropped
• Make sure you box your final answers and match problem parts accurately in Gradescope, or you will be deducted 5% of the corresponding problem part.
• Make sure that your homeworks are neat enough to read. Graders has the flexibility to deduct points for lack of neatness.
• Homeworks constitute an essential component of your learning experience in the course and prepare you for your quizzes/exam in effective ways. Investing time to do your homeworks with care will pay off when you are taking your quizzes/exam.
  • You will be expected to provide detailed explanations of your solutions in order to obtain full credit in your homeworks. Conversely, solutions lacking full explanations will receive zero credit even when the answer provided may be correct and further incorrect answers without any work shown may lead to an academic integrity violation case being opened against you and a sanction of at least a letter grade reduction in the course.
  • You are encouraged to collaborate to understand the problems in the homework, but each student should solve the problems individually and independently for submission even if they work together initially to understand how to solve the problems. Copying a joint solution is not acceptable and may lead to an academic integrity violation case being opened against you and a sanction of at least a letter grade reduction in the course.
  • It is acceptable to use online resources to understand the problems in the homework, but each student should solve the problems independently for submission. Copying or 'following' the online solution is not acceptable and may lead to an academic integrity violation case being opened against you and a sanction of at least a letter grade reduction in the course.
  • Posting or sharing your solutions (Discord, email, photocopies, etc.) is not acceptable and may lead to an academic integrity violation case being opened against you and a sanction of at least a letter grade reduction in the course.
  • Any of these academic integrity violations will result in at least a letter grade reduction, and possibly stronger sanctions. It is not worth the risk for what each problem in the HWs is worth, and it will not help you learn the course material.
  • Please keep these cautionary remarks in mind as you are working out your homeworks and avoid submitting unsubstantiated solutions to avoid any misinterpretations as explained above.
• Solutions will be posted in Canvas 50 minutes after the deadline (to accommodate late penalized submissions).
• Regrades: You will receive an email from Gradescope so you can log in and see your graded homework. If after looking at the posted solutions, you feel there was an inaccuracy in the grading of your homework, you can request a regrade within Gradescope itself. Make sure you submit regrade requests within a week after your graded homework is made available via Gradescope. Regrades will not be accepted after that date.

DRES: Students with documented disabilities must notify the instructor by June 17.

OFFICE HOURS

Summary of office hours times, from June 14 to August 3, except June 17 and July 4.

Zoom link for all office hours is in Canvas.

*NOTE: If you want to come by in-person, you must notify the corresponding staff member at least 1 hour beforehand. Staff emails are here.

*NOTE: If you want to come by in-person, you must notify the corresponding staff member at least 1 hour beforehand. Staff emails are here.

QUIZZES AND EXAM INFORMATION

There will be weekly quizzes on Tuesdays, except July 5th (quiz will be on July 6 instead) and there will be a final exam on Saturday, August 6, 3.30-5.30pm CDT.

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 8am CDT on the day of the quiz.

In-person quizzes/exam will take place in ECEB 1013.

Links for online quizzes are in Canvas.

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

Quiz and exam dates:

• Quiz 1: June 21, 2pm CDT, or at 8pm CDT.
• Quiz 2: June 28, 2pm CDT, or at 8pm CDT.
• Quiz 3: July 6, 2pm CDT, or at 8pm CDT.
• Quiz 4: July 12, 2pm CDT, or at 8pm CDT.
• Quiz 5: July 19, 2pm CDT, or at 8pm CDT.
• Quiz 6: July 26, 2pm CDT, or at 8pm CDT.
• Quiz 7: August 2, 2pm CDT, or at 8pm CDT.
• Final Exam: Saturday, August 6, 3.30-5.30pm CDT.

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 17.

• 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 a sanction of at least a letter grade reduction in the course.


• Allowed materials: no resources (notes, slides, etc.) are allowed; otherwise, an Academic Integrity report will be filed against you and a sanction of at least a letter grade reduction in the course.


• 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 a sanction of at least a letter grade reduction in the course.

• Proctoring:
  • You will need two devices with internet capability, one for you to look at the quiz/exam pdf on Gradescope and another one that will connect to Zoom so the proctor can monitor you.
  • The proctor will also need to be able to see the screen of the device where you will look at the pdf. Here is CBTF's camera positioning handout, so please look at it and make sure you can position your camera correctly (you might need to prop it with something) so we can see your workspace, your computer and your hands and face.
  • You will have to make sure that the device you will use for Zoom has the camera, microphone and speakers working so you can receive instructions before and during the quiz/exam, and so we can hear your surroundings during the quiz/exam.
  • Please identify an appropriate place for you to take the quiz/exam, which should be quiet because you will have your microphone on so we can monitor the audio around you. When you join the Zoom session you will be asked to allow the host to unmute you and you must allow it.
  • Failure to comply with these rules will cause you to receive a zero in the quiz/exam.


• Solving the quiz/exam: you must solve the quiz/exam on blank sheets of paper. Tablets are not allowed for writing and you may not print the quiz/exam; otherwise, an Academic Integrity report will be filed against you and a sanction of at least a letter grade reduction in the course.
  You must include ALL your work in your upload to get credit and to avoid an Academic Integrity report being filed against you and a sanction of at least a letter grade reduction in the course.


• Solution uploads: Once the quiz/exam time is over, you will have an additional 5 minutes to upload your solutions to Gradescope. You will be deducted 25% per extra minute after that.
  • 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.
  • 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. We will not accept your quiz/exam if you leave the proctoring session before finishing your submission to Gradescope, and you will get a zero in the quiz/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 quiz/exam to save time.
  • Gradescope will timestamp when the document is uploaded, so you can then take some additional time assigning your answers to the questions, like you do in your HW


• An Academic Integrity report will be filed against you and a sanction of at least a letter grade reduction in the course for unauthorized actions.

GRADING POLICIES

• 16% HW (will drop your worst two HW grades)
• 54% Weekly quizzes (will drop your worst quiz grade)
• 30% Final Exam

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

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

• 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)

• 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 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.

TOPICS

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

Concept constellation

Content from notes:

• Chapter 1: Foundations
  • 1.1 Embracing uncertainty
  • 1.2 Axioms of probability
  • 1.3 Calculating the size of various sets
  • 1.4 Probability experiments with equally likely outcomes
  • 1.5 (Skip) Sample spaces with infinite cardinality
• Chapter 1:Discrete-type random variables
  • 2.1 Random variables and probability mass functions
  • 2.2 The mean and variance of a random variable
  • 2.3 Conditional probabilities
  • 2.4 Independence and the binomial distribution
    • 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
  • 2.5 Geometric distribution
  • 2.6 (Skip) Bernoulli process and the negative binomial distribution
  • 2.7 The Poisson distribution
  • 2.8 Maximum likelihood parameter estimation
  • 2.9 (Skip) Markov and Chebychev inequalities and confidence intervals
  • 2.10 The law of total probability, and Bayes formula
  • 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
  • 2.12 Reliability
    • 2.12.1 Union bound
    • 2.12.2 Network outage probability
    • 2.12.3 Distribution of the capacity of a flow network
    • 2.12.4 (Skip) Analysis of an array code
    • 2.12.5 Reliability of a single backup
• Chapter 3: Continuous-type random variables
  • 3.1 Cumulative distribution functions
  • 3.2 Continuous-type random variables
  • 3.3 Uniform distribution
  • 3.4 Exponential distribution
  • 3.5 (Skip) Poisson processes
    • 3.5.1 (Skip) Time-scaled Bernoulli processes
    • 3.5.2 (Skip) Definition and properties of Poisson processes
    • 3.5.3 (Skip) The Erlang distribution
  • 3.6 Linear scaling of pdfs and the Gaussian distribution
    • 3.6.1 Scaling rule for pdfs
    • 3.6.2 The Gaussian (normal) distribution
    • 3.6.3 The central limit theorem and the Gaussian approximation
  • 3.7 ML parameter estimation for continuous-type variables
  • 3.8 Functions of a random variable
    • 3.8.1 The distribution of a function of a random variable
    • 3.8.2 Generating a random variable with a specified distribution
    • 3.8.3 (Skip) The area rule for expectation based on the CDF
  • 3.9 (Skip) Failure rate functions
  • 3.10 Binary hypothesis testing with continuous-type observations
• Chapter 4: 4 Jointly Distributed Random Variables
  • 4.1 (Skip) Joint cumulative distribution functions
  • 4.2 Joint probability mass functions
  • 4.3 Joint probability density functions
  • 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
  • 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
  • 4.7 (Skip) Joint pdfs of functions of random variables
    • 4.7.1 (Skip) Transformation of pdfs under a linear mapping
    • 4.7.2 (Skip) Transformation of pdfs under a one-to-one mapping
    • 4.7.3 (Skip) Transformation of pdfs under a many-to-one mapping
  • 4.8 Correlation and covariance
  • 4.9 Minimum mean square error estimation
    • 4.9.1 Constant estimators
    • 4.9.2 Unconstrained estimators
    • 4.9.3 Linear estimators
  • 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 (Skip) Joint Gaussian distribution
    • 4.11.1 (Skip) From the standard 2-d normal to the general
    • 4.11.2 (Skip) Key properties of the bivariate normal distribution

ADDITIONAL RESOURCES

• Registration deadlines, add/drop course deadlines, advising schedules, and finals
• Academic integrity
• Inclusivity
• Disability Resources and Educational Services (DRES)
• FERPA
• Sexual misconduct
• Support Resources and Supporting Fellow Students in Distress
• Run, hide, fight
• 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.

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.

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 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.

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

• police.illinois.edu/safe for more information on how to prepare for emergencies, including how to run, hide or fight and building floor plans that can show you safe areas.
• emergency.illinois.edu to sign up for Illini-Alert text messages.
• Follow the University of Illinois Police Department on Twitter and Facebook to get regular updates about campus safety.