ECE 313/MATH 362


Summer 2019

Slides --- Video lectures --- HW (Masterprobo) --- Office hours --- Exams --- Tentative topic schedule --- Grading Policies --- Piazza --- Staff --- FAQ --- COMPASS

ECE 313 (also cross-listed as MATH 362) is an 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

Course information in course explorer

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Summary of office hours times and locations, from June 12 to August 1.
Hours Monday Tuesday Wednesday Thursday
except July 4
11am-12pm 3034 ECEB 3034 ECEB 3034 ECEB
3-5pm 3034 ECEB 3034 ECEB 3034 ECEB
6-7pm Zoom link for this office hour Zoom link for this office hour Zoom link for this office hour
7-8pm Zoom link for this office hour
8-9pm Zoom link for this office hour

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Section Meeting time and place Instructor
1013 ECE Building
Juan Alvarez
e-mail: alvarez AT illinois dot edu
Office Hours:
Mondays, 11-11.50am, 3034 ECEB.
Wednesdays, 11-11.50am, 3034 ECEB.
Thursdays, 11-11.50am, 3034 ECEB.

Graduate Teaching Assistant:s
Ali Yekkehkhany (yekkehk2 AT illinois dot edu) Office Hours: Mondays, 3-5pm, 3034 ECEB,
Wednesdays, 3-5pm, 3034 ECEB,
Thursdays, 3-5pm, 3034 ECEB.
Kiwook Lee (klee137 AT illinois dot edu) Office Hours: via Zoom, Monday 6-8pm, Tuesday-Wednesday, 7-8pm.
Amr Martini (ammartn3 AT illinois dot edu) Office Hours: via Zoom, Tuesday-Wednesday 6-7pm, Thursday 6-8pm.
Shiyi Yang (yang158 AT illinois dot edu) Office Hours: via Zoom, Monday-Thursday, 8-9pm.

Office hours for online students will be done using Zoom. Make sure you create an account and get familiar with it.

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checkpoint #
checkpoint deadline
Concepts (Notes sections)[Short videos]
1 Monday,
June 17
* 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 principles of counting and over counting; binomial coefficients (Ch 1.3-1.4) [ILLINI, SAQ 1.3, SAQ 1.4, PokerIntro, PokerFH2P]
* using Karnaugh maps for three sets (Ch 1.4)[Karnaughpuzzle, SAQ1.2]
2 Thursday,
June 20
* 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]
3 Thursday, June 27 * 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]
* 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]

Exam 1: Wednesday, June 26. Main exam: 10-10.50am, conflict exam (only available for online students): 8-8.50pm.
4 Monday,
July 1
* Maximum likelihood parameter estimation (definition, how to calculate for continuous and discrete parameters) (Ch 2.8) [SAQ 2.8][hypergeometric]
* Markov and Chebychev inequalities (Ch 2.9)
* confidence intervals (definitions, meaning of confidence level) (Ch 2.9)[SAQ 2.9,Simdoc-Minhash2]
* law of total probability (Ch 2.10) [deuce] [SAQ 2.10]
* Bayes formula (Ch. 2.10)
5 Wednesday,
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]
* network outage probability, distribution of capacity and more applications of the union bound (Ch 2.12.2-2.12.4)

NO lecture on Thursday, July 4.

Exam 2: Wednesday, July 10. Main exam: 10-10.50am, conflict exam (only available for online students): 8-8.50pm.
6 Thursday,
July 11
* cumulative distribution functions (Ch 3.1)[SAQ 3.1]
* probability density functions (Ch 3.2) [SAQ 3.2][simplepdf]
* uniform distribution (Ch 3.3) [SAQ 3.3]
* exponential distribution (Ch 3.4) [SAQ 3.4]
7 Thursday,
July 18
* Poisson processes (Ch 3.5) [SAQ 3.5]
* Erlang distribution (Ch 3.5.3)
* 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]
8 Monday,
July 22

* 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]
* 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)
* failure rate functions (Ch 3.9)[SAQ 3.9]
* binary hypothesis testing for continuous type random variables (Ch 3.10) [SAQ 3.10]
9 Thursday,
July 25
* joint CDFs (Ch 4.1)[SAQ 4.1]
* joint pmfs (Ch 4.2)[SAQ 4.2]
* joint pdfs (Ch 4.3)[SAQ 4.3]

Exam 3: Wednesday, July 24. Main exam: 10-10.50am, conflict exam (only available for online students): 8-8.50pm.
10 Monday,
July 29
* joint pdfs of independent random variables (Ch 4.4)[SAQ 4.4]
* distribution of sums of random variables (Ch 4.5)[SAQ 4.5]
* more problems involving joint densities (Ch 4.6)[SAQ 4.6.]
- Skip Section 4.7.
11 Friday,
August 2

* 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)

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Exams will be open book.

Exams for online students will be proctored using Zoom. Make sure you create an account and get familiar with it.

You can find copies of old midterm exams and final exams here. The exams this semester might not be similar in nature as in recent past semesters because of them being open book.

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.

The topics covered in Exam 2 are exactly the ones in the course notes up until (and including) section 2.12, except for Sections 1.5 and 2.9, with emphasis on Chapter 2. You should know the meanings, forms, means, and variances for the key discrete distributions.

The topics covered Exam 3 are exactly the ones in the course notes up until (and including) section 3.10, except for Sections 1.5, 2.9, and 3.9, with emphasis on Chapter 3. You should know the meanings, forms, means, and variances for the key discrete and continuous distributions.

The final exam will cover the topics in the notes through Section 4.9.3, except for Sections 1.5, 2.9, 3.9, and 4.7, with emphasis on Chapter 4. You should know the meanings, forms, means, and variances for the key discrete and continuous distributions..

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 when you receive your graded midterm exam, and after looking at the posted solutions, you feel there was an inaccuracy in the grading of your exam, fill out an exam regrade request form and staple it to your exam BUT do not write on or alter in any way your original exam paper. Turn in such regrade requests to your instructor by the end of the third lecture after the graded exam is handed back.

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.

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

  • 15% Homework (Masterprobo, two checkpoints 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.),

  • 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.

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Link to MasterProbo.

  • Q: How do I access MasterProbo?
    A: Follow the above link. Click "Register" button on the upper-right corner. Enter your NetID and a preferred password. You will receive an activation e-mail in your illinois mailbox. Follow the link to activate your account.
  • Q: What are the checkpoint deadlines?
    A: 11:59pm of each deadline date. The list of checkpoint deadline dates are in the tetative topic schedule table.
  • Q: What do I do if MasterProbo says I am not enrolled?
    A: If you enrolled recently, please e-mail with [enrollment] in the subject line for timely response. For instance: "[enrollment] can't access masterprobo". Response might be delayed for e-mails without proper subject line.
  • Q: Can I go back to a previous week's module?
    A: Yes, if you have not achieved mastery, you can practice at any time. But you can't increase your score for a given week after the deadline. The Past Problems tab is unlocked after each due date.
  • Q: Does receiving a probo mean I got full credit for that section?
    A: No. It's one probo for each goal. A module (section) can have multiple probos (goals).
  • Q: Do I need to fill the bar to get full credit?
    A: The bar indicates mastery. You do not need to fill the bar to get probos, but you are encouraged to achieve mastery. Will make life easier in later modules and exams.
  • Q: Does the proficiency number I see affect my grade?
    A: No, it does not affect your grade. But it's a good way for you to keep track of where you are.
  • Q: What are probos?
    A: Probos are points that are converted to homework grades at each checkpoint deadline: You receive 3 probos when you complete a module such as Counting.
  • Q: What will be my homework score if I only earned 6/8 probos for a checkpoint?
    A: Your homework score will be pro-rated. For instance, the full score is 10, and you will receive 10*6/8 = 6.7 for this checkpoint.
  • Q: If I fall sick during a week and am unable to pass the checkpoint, can I ask for an extension?
    A: Since we are dropping your two lowest scores, there will be no extension of deadlines.
  • Q: How is MasterProbo different from, say, WebAssign?
    A: MasterProbo is a personalized learning tool that detects your weakness and tries to strengthen it.
  • Q: Do I still need to read the course notes now that we have MasterProbo?
    A: You need to have the basic concepts to understand the problem... MasterProbo tries to improve your mathematical thinking, but you need to know what to think about.
  • Q: How many problems are there in each module?
    A: The number of problems you will work on to reach proficiency varies. Generally speaking, if you solve a difficult problem, you gain more proficiency. However, it might not be the most time-efficient as you can get stuck on difficult problems. It is advised you start early.
  • Q: If I get stuck and SOS, will the TA give me the answer?
    A: No, the TAs will give you personalized hints to help you think, but they will not give you the answer.
  • Q: How do I report a bug in Masterprobo while I am working on a problem?
    A: If you need clarification on the wording, or a problem is not displayed correctly, the "report a problem" button on the upper-left corner is the best way to report such issues.
  • Q: How do I report other technical issues?
    A: E-mail with [technical] in your subject line. (e.g., server not responding, didn't receive activation e-mail). For instance: "Subject: [technical] no activation e-mail". Response might be delayed for e-mails without proper subject line.

Technical support

Desktops and Laptops

  • Preferred browser: Chrome (Windows 10 and Mac OS X)
  • Other browsers: Safari, Edge. (No problem detected, but not as extensively tested) There is a known problem with Firefox.

Mobile (not recommended)

  • We do not provide support for mobile

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Lectures will be recorded daily and displayed at

You can access this site by entering your University of Illinois email address. They’ll you will be prompted to authenticate using your Active Directory (AD) password. Once you’re authenticated, you should see a dashboard page displaying content for which you are enrolled as a student.

Further documentation on how to use the Echo360 platform can be found at