Math 461, Section C13, Probability
Spring 2012

Course Information


Professor:Kay Kirkpatrick
Office:334 Illini Hall
Contact:The way to get in touch with me is by email, kkirkpat(at)illinois.edu, with subject line "Math 461 ...", and with salutation "Dear Professor Kirkpatrick".
Lectures: MWF 10:00-10:50 (347 Altgeld Hall)
Office hours: Mondays and Wednesdays, 11:00-11:50, or by appointment. I would be happy to answer your questions in my office anytime as long as I'm not otherwise engaged, and before and after class are good times to catch me either in my office or in the classroom. Office hours the first two weeks will be 1/18 & 1/20 at 11am, and 1/27 at 9am (and as announced by the guest lecturer).
Textbook: Sheldon Ross, A First Course in Probability, 8th Edition. 2008, Prentice Hall. (It is okay to use an old edition for studying, but the homework problems will be from the 8th edition, and you can check my textbook or a classmate's to make sure you're doing the right problems.)
Homework policy: Homework will be assigned regularly, and collected on Fridays in class. You are encouraged to work together on the homework, but I ask that you write up your own solutions and turn them in separately. Late homework will not be graded, and if for some reason you've done a homework but can't turn it in in class, you should turn it in to my mailbox before class, or ask a classmate to turn it in for you. Because of this strict policy on late homework, I will drop your two lowest homeworks.
Homework philosophy: Mathematics is not a spectator sport, so it is important that you do the homework. Doing homework problems and explaining them to each other is the best way to really learn the material, so I encourage you to work together on the homework. If, after thinking and talking about homework problems, you have questions or get stuck, I will be happy to help you in my office. I also have the philosophy that you will learn the material best if you come to class and read the textbook before and/or after class, even if you can learn the material from the textbook alone. (This textbook is full of examples, and sometimes it's hard to figure out what is important.) You can maximize your chances of doing well in this class by combining all of these resources: lectures, textbook, homework, office hours, and discussions with classmates.
Exams: There will be two in-class midterm exams, scheduled for February 24th and tentatively April 6th. Each exam will be technically comprehensive, but emphasizing recent material up to the most recent graded and returned homework assignment, and exam problems will be very similar to homework problems. The final exam is: 8:00-11:00 AM, Tuesday, May 8th. It will cover the most important topics of the whole course, emphasizing recent material somewhat.
Exam policy: Make-up exams will be given only for medical or other serious reasons. If you discover that you cannot make it to an exam, please let me know as soon as possible, so that we can make other arrangements.
Grading policy: Homework: 10% of the course grade
2 Midterms: 25% each
Final Exam: 40%
There will probably be a curve for the final letter grades, but at worst, 93% would be the highest cutoff for an A, 90% for an A-, 87% for a B+, and so on.

Homework assignments (to be updated)

HW #1, due Friday, January 20 before class: please send me an email introducing yourself: for instance, your major, where you're from, your hobbies, why you're interested in probability, what you hope to get out of this class, or anything else you want to share or have questions about.

HW #2, due Friday, January 27 in class: Ch. 1 (pp. 16-17): 4, 5, 7, 8, 11, 12, 18, 19, 20, 21, 24, 27, and Ch. 2 (pp. 50-51): 2, 3, 5, 6 Answers

HW #3, due Friday, February 3 in class: Ch. 2 (pp. 50-51): 7, 8, 9, 12, 17, 18, 20, 21, 25, 27, 28, 32, 37, 43 Answers

HW #4 due Friday, February 10 in class: Ch. 2 (pp. 50-51): 50, 53, 54, and Ch. 3 (pp. 102ff): 1, 5, 6, 9, 10, 20, 23, 30, 47, 51, 56, 57, 59. Answers

Solutions to the Diagnostic

HW #5 due Friday, February 17 in class: Ch. 3 (pp. 107ff): 64, 66, 78, 81, 83, 84, and Ch. 4 (pp. 172ff): 1, 4, 5, 13, 14, 17, 19 (in these last two problems, "distribution function" means cumulative distribution function) Answers

Friday, February 24: first exam in class (no HW due). Please contact me asap if you are not able to attend the exam. There are several things to help you study: HW answers and the solutions to the Diagnostic above. Also, what the exam will cover: HW #2-5, and material from chapters 1 through 4, up through section 4.7, including definitions of fundamental concepts, but not proofs. For the material of chapter 4 that is covered on the exam but hasn't been represented in the homework yet, you are responsible only for what we've done in class. Here's a sample exam with solutions, if that helps you study. Caveat downloader: this is borrowed from someone else, and my exam may be a bit different.

Midterm 1 with solutions

HW #6 due Friday, March 2 in class: Ch. 4 (pp. 172ff): 21, 23, 32, 35, 37, 38, 40, 42, 45, 48, 50. Answers

HW #7 due Friday, March 9 in class: Ch. 4 (pp. 172ff): 55, 57, 59, 61, 63, 72, 73, 77, 78, 79, 84, 85. Ch. 5: 1, 2, 4, 5. Answers

No HW due Friday, March 16

HW #8 due Friday, March 30 in class: Ch. 5: 6, 10, 12, 13, 15, 18, 21, 22, 23, 25, 28, 32, 33, 34, 37, 38, 40, 41. Ch 6: 2, 7, 8, 9, 10. Answers

Friday, April 6: second exam in class (no HW due). Here are some study tips from Richard Laugesen:
  • Make an outline, with the main definitions and methods from each section.
  • Review the summary sheets for discrete and continuous distributions, reminding yourself of their pmf/pdf formulas, expectations, and variances. (The hypergeometric and Cauchy distributions are cool but not your responsibility.)
  • Review the physical/engineering interpretation of each random variable (e.g., the waiting time for a Poisson event is an exponential RV).
  • After doing all that review, then you will benefit from re-working homework problems and in-class examples, because then you will have an improved mental framework to fit the problems into.
  • Work through the practice exam, keeping in mind that our exam will be different.

    HW #9 due Friday, April 13 in class: Ch. 6: 11, 13, 14, 18, 20, 21, 22, 23, 27, 28, 29, 31, 33. Answers

    HW #10 due Friday, April 20 in class: Ch. 6: 38, 40, 41, 42, 48, and Ch. 7: 5, 6, 7, 8, 11, 18, 19, 21. Answers

    UPDATE: last HW #11 due Friday, April 27 in class: Ch. 7: 30, 31, 33, 38, 39, 41, 42, 50, 51, 56, 57. Answers

    Suggested homework problems not to be turned in, but as practice for the final: Ch. 7: 75, Ch. 8: 1, 2, 4, 5. Answers

    Research opportunities announced in class: I'm open to Honors Credit Learning Agreements involving projects connecting probability to the real world and to your interests. Please email me if you're interested.


    Schedule of material covered (to be updated)

    Week 1: Introduction, sections 1.2, 1.3, 1.4, 1.6
    Week 2: Guest lectures Monday and Wednesday, sections 1.5, 2.2-2.5
    Week 3: Sections 2.5, 3.2-3.4
    Week 4: Sections 3.4, 4.1, 4.2, 4.10
    Week 5: Guest lectures Monday and Wednesday, sections 4.3-4.6
    Week 6: Sections 4.7, 4.8, Review, Exam #1 scheduled for Feb. 24 during the usual class time (please contact me asap if you are not able to attend the exam).
    Week 7: Sections 4.8-4.9, 5.1-5.3
    Week 8: Sections 5.4-5.7
    Week 9: Sections 5.7, 6.1
    Week 10: (Spring break)
    Week 11: Sections 6.2-6.5
    Week 12: Section 6.5-6.6, review, and Exam #2 scheduled for Apr. 6. Please contact me asap if you might not be able to attend the exam.
    Week 13: Sections 7.2-7.4
    Week 14: Sections 7.5-7.7
    Week 15: Sections 7.7, 8.2-8.3
    Week 16: Section 8.3 (last day of class: May 2)
    Final exam: 8:00-11:00 AM, Tuesday, May 8th.

    Outline of approximate time to spend on each chapter:
    Chapter 1, Combinatorial Analysis, 4 hours
    Chapter 2, Axioms of Probability (omit sections 2.6, 2.7), 4 hours
    Chapter 3, Conditional Probability and Independence (omit section 3.5), 4 hours
    Chapter 4, Random Variables (omit subsection 4.8.4), 6 hours
    Chapter 5, Continuous Random Variables (omit subsections 5.5.1, 5.6.2, 5.6.4), 7 hours
    Chapter 6, Jointly Distributed Random Variables (omit sections 6.6, 6.8), 5 hours
    Chapter 7, Properties of Expectations (omit subsections 7.2.1, 7.2.2, 7.7.1, and section 7.9), 7 hours
    Chapter 8, Limit Theorems (omit sections 8.4, 8.5, 8.6), 3 hours
    Exams and leeway, 5 hours
    We will use important topics from calculus, such as infinite series with positive terms (most calculations involve the geometric series and series derived from it), improper integrals and double integrals (change of variables formula, manipulating Gaussian integrals).

    Holidays

    This semester we will not have classes on March 19-23 (spring break).

    Syllabus

    Introduction to mathematical probability: includes the calculus of probability, combinatorial analysis, random variables, expectation, distribution functions, moment-generating functions, and the central limit theorem. We will cover most of the material in the first eight chapters of the textbook.

    Why study probability?

    Two main reasons: uncertainty and complexity. Uncertainty is all around us and is usefully modeled as randomness: it appears in call centers, electronic circuits, quantum mechanics, medical treatment, epidemics, financial investments, insurance, games (both sports and gambling), online search engines, for starters. Probability is a good way of quantifying and discussing what we know about uncertain things, and then making decisions or estimating outcomes. Some things are too complex to be analyzed exactly (like weather, the brain, social science), and probability is a useful way of reducing the complexity and providing approximations. And the reason I study probability: statistical mechanics, which combines both the uncertainty of quantum mechanics, and the complexity of zillions of particles interacting.