Math 461
Probability
Spring 2015

Course webpage: https://faculty.math.illinois.edu/~kkirkpat/461spr2015.html


Professor:Kay Kirkpatrick
Contact:The way to get in touch with me is by email, kkirkpat(at)illinois.edu, with 461 in the subject line and addressing me as "Professor Kirkpatrick."
Time and place: Section M13 at 09:30AM - 10:50AM on TR in 445 Altgeld Hall
Section Q13 at 12:30PM - 01:50PM on TR in 141 Altgeld Hall
Office hours: Tuesdays and Thursdays 3:00-3:50 pm, or by appointment, in my office, 334 Illini Hall. I'm happy to answer your questions anytime that I'm not otherwise engaged; before and after class are good times to catch me either in my office or in the classroom.
Textbook: Sheldon Ross, A First Course in Probability, 9th Edition, 2012, Prentice Hall. Other editions are okay for studying; the homework problems will be from the 9th edition, which you can check against my textbook or a classmate's. (Page numbers are the main difference.)
Homework policy: Homework will be assigned regularly and collected in class, or turned in to my mailbox in 250 AH before class. You are encouraged to work together on the homework, but you should write up your own solutions to turn in separately. If you use two names, put both of them on your homework. Late homework will not be graded; instead I will drop your two lowest scores.
Homework philosophy: Mathematics is something that you learn by doing: doing homework problems and explaining them to each other. If, after thinking about them, you get stuck or have questions, I will be happy to help. You'll have a high probability of doing well in this class by combining all of these resources: classes, textbook, homework, office hours, and discussions with classmates.
Exams: Two in-class midterms are scheduled for February 26 and April 9. Each exam will be comprehensive, emphasizing recent material up to the most recent graded and returned homework assignment. The final exam will cover important topics of the whole course, emphasizing recent material somewhat. The final is a combined final exam for Math 461 (sections M13/M14 and Q13/Q14) and will be held 1:30-4:30 pm on Friday, May 8, 2015 in room 213 Greg Hall. The Math 461 conflict exam is Friday morning, May 8, 2015: email me for coordinates. (NOTE: these combined final and conflict exams replace the other final exam times.)
Exam policy: Make-up exams will be given only for medical or other serious reasons, and arrangements should be initiated by you as soon as possible. You must work completely on your own during exams and quizzes. My exams are fair and similar to homework, so as long as you use the resources provided, you should be fine. If you have difficulties or fall behind in the course, please come talk to me.
Grading policy: Homework: 20% of the course grade
2 Midterms: 20% each
Final Exam: 40%
There will probably be a curve for the semester letter grades; 90% would be the highest cutoff for an A-, 80% for a B-, and so on. If you are near a cutoff, I take your lecture participation into account.
Classroom policy: I support individuals with diverse backgrounds, experiences, and ideas across a range of social groups including race, ethnicity, gender identity, sexual orientation, abilities, economic class, religion, and their intersections. I expect that we will all treat each other with respect. Please contact me to request disability accommodations.
Prerequisites: Math 241 or the equivalent. We will use topics from calculus, such as geometric series, improper and double integrals, and changes of variables.

Homework assignments (to be updated)

HW #0, due Thursday, January 22 by 5pm: please send me an email introducing yourself: for instance, what name you prefer to be called, your major and hobbies, why you're interested in probability, or anything else you want to share or have questions about. It would also be helpful to attach a photo of yourself to help me connect your face with your name.

HW #1, due Thursday, January 29 in class: Ch. 1 (pp. 15-17): 4, 5, 7, 8, 12, 18, 19, 20, 21, 24, 27, and Self-test problem 7 (p. 19); Ch. 2 (p. 48): 2, 3, 5 Answers

HW #2, due Feb 5 in class: Ch. 2 (pp. 48ff): 7, 8, 9, 12, 17, 18, 20, 21, 25, 27, 28, 32, 37 Answers

Some problem-solving tips from the book "How to Solve it" by Polya

HW #3, due Feb 12 in class: Ch. 2 (p. 51): 50, 53, and Ch. 3 (pp. 97ff): 1, 5, 6, 9, 10, 20, 23, 30, 47, 51, 56, 57, 59. Answers

There will be a quiz on Thursday Feb 19, approximately 20 minutes, two problems, over HWs 1-3. If you do well on the quiz, it will replace one of your low HW scores; if not, I'll drop the quiz.

HW #4, due Feb 19 in class: Ch. 3: 64, 66, 78, 81, 83, 84, and Ch. 4 (pp. 163ff): 1, 4, 5, 13, 14, 17, 19. Answers

Old Midterm 1 with solutions
Solutions for Midterm 1

Midterm 1 covers homework problems up through and including HW #4 and lectures through Feb. 24. This means that the material in sections up through 4.2 and 4.10 will be examined more thoroughly than the material in sections 4.3-4.8 (for which you are responsible for the main facts and examples from lectures). Homework problems on 4.3-4.6 will be on Midterm 2.

HW #5 due March 5 in class: Ch. 4 (pp. 163ff): 21, 23, 32, 35, 37 Answers

HW #6 due March 12 in class: Ch. 4: 38, 40, 42, 45, 48, 50, 55, 57, 59, 61, 63, 72, 73, 77, 78, 79, 84, 85. Ch. 5: 1, 2, 4, 5 Answers

HW #7 due March 19 in class: Ch. 5: 6, 10, 12, 13, 15, 18, 21, 22, 23, 25, 28, 32, 33, 34 Answers

HW #8 due April 2 in class (turn in to the guest lecturer): Ch. 5: 37, 38, 40, 41. Ch 6: 2, 7, 8, 9, 10 Answers

Midterm 2 covers homework problems up through and including HW #8 and lectures through Apr. 7. This midterm is comprehensive but emphasizes material not covered on Midterm 1, the earliest of which is lecture material on 4.8 and homework problems on 4.3-4.6.

Here are some study tips from Richard Laugesen:
  • Make an outline with definitions and techniques from each section.
  • Review the summary sheets for discrete and continuous distributions, their pmfs or pdfs, expectations, variances, and practical applications. (Hypergeometric and Cauchy are cool but not the most important.)
  • After that review, 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 April 16 in class: Ch. 6: 13, 14, 20, 21, 22, 23, 27, 28, 29, 33. Also, the bonus problem from Midterm 2: what is the pdf of X^2+Y^2 if X and Y are independent standard normals? Hint: compute directly using polar coordinates: the cdf of Z = X^2 + Y^2 is P(X^2 + Y^2 < = R^2) = a double integral over the radius-R disc of the joint pdf (which is the product of two standard normal pdfs). Then take the derivative to get the pdf of Z, and you should recognize it. Answers

    HW #10 due April 23 in class: Ch. 6: 38, 40, 41, 42, 48, and Ch. 7: 5, 6, 7, 8, 11, 19, 21. Answers

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

    Old final for studying.

    ANNOUNCEMENT: The combined final exam for Math 461 (sections M13/M14 and Q13/Q14) for the Spring 2015 will be held 1:30-4:30 pm on Friday, May 8, 2015 in room 213 Greg Hall. The Math 461 conflict exam will be held Friday morning, May 8, 2015: email me for coordinates. (NOTE: these combined final and conflict exams replace the other final exam times.)


    Schedule for lectures

    Week 1: Introduction, sections 1.2-1.6, 2.2-2.3
    Week 2: Sections 2.2-2.5, 3.2
    Week 3: Sections 3.3-3.4
    Week 4: Sections 4.1, 4.2, 4.10
    Week 5: Sections 4.3-4.6
    Week 6: Sections 4.7, 4.8, review, Midterm 1 on February 26
    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--no class)
    Week 11: Sections 6.2-6.5
    Week 12: Section 6.5-6.6, review, Midterm 2 on April 9
    Week 13: Sections 7.2-7.3, 7.7
    Week 14: Sections 7.4-7.5
    Week 15: Sections 7.6-7.7, 8.2-8.3
    Week 16: Section 8.3, review (last day of class: May 5)

    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.

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