Homework assignments (to be updated)
HW #0, due by 5pm the first Friday of classes: 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 by the end of class on Friday, Jan. 25 (in class or in my
mailbox in Altgeld 250): Ch. 1 (pp. 15ff):
12, 18, 24, 27, and Ch. 2 (pp. 48ff): 2, 3, 5, 7, 8, 9, 12, 17, 18, 20.
Some problem-solving tips from the book "How to Solve it" by Polya
Note: please write your section number or section time at the top of your HW.
HW #2, due by the end of class Friday, Feb. 1: Ch. 1 (pp. 15ff): 4,
5, 7, 8, 19, 20; Ch. 2 (pp. 48ff): 21, 25, 27. Another three
problems, 28, 32, 37, are recommended but not required for HW #2.
Answers
HW #3, due Feb 8 in class: Ch. 2 (p. 51): 37, 50, 53, and Ch. 3
(pp. 97ff): 1, 5, 6, 9, 10, 20, 23, 30, 47, 51, 56, 57.
Answers
HW #4, due Friday Feb 15 by the end of class: Ch. 3: 66, 78,
81, 83, 84, and Ch. 4 (pp. 163ff): 1, 5, 13, 14, 17, 19. Please
remember to write your section number or time at the top of your
HW.
Answers
Note: there will be a quiz in class on February 15, one week before
the first midterm. The quiz will cover all of the HWs that have been
graded and returned beforehand. If you do well on the quiz, it will replace one of your low HW scores; if not, I'll drop the quiz.
Here are some study tips from Richard Laugesen:
Make an outline with definitions and techniques from each
section.
Review the summary sheet for
discrete
distributions, their pmfs,
expectations, variances, and practical applications. (Pay attention
to the ones that we have covered; you're not responsible for
Geometric, Negative Binomial, and Hypergeometric on Midterm 1.)
After that review, you will benefit from re-working
homework problems, in-class examples, and the practice midterm, because then you will have an
improved mental framework to fit the problems into.
Old (practice) Midterm 1 with solutions
No HW due on the day of the midterm. Midterm 1 covers homework problems up through and including HW #4 and lectures
through Feb. 18. This means that the material in sections up through
early Chapter 4 material
will be examined more thoroughly than the material in later
Chapter 4 sections, e.g., 4.6-4.8 (for which you are only responsible for the things
from lectures). Homework problems on 4.3-4.6 will be on Midterm 2.
HW #5, due Friday Mar 1 by the end of class: Ch. 4 (pp. 163ff): 21,
23, 32, 35, 37, 38, 40, 42
Answers
Important note: If you want to turn in your homework during class and
you're unable to stay for lecture (which is fine, because I don't make
attendance mandatory, as you know), then please turn your HW in to my
mailbox in Altgeld 250. Also please write your section number or time
on your HW.
HW #6, due Friday Mar 8 by the end of class: Ch. 4: 48, 50, 55, 57, 59, 61,
63, 72, 73, 77, 78, 79, 85. Ch. 5: 1, 2, 4, 5.
Answers
There will be guest lecturers on 3/6 (Partha Dey), 3/8 (Lee DeVille),
3/13 (Dey), and 3/15 (Richard Sowers) because I have two conferences
at which I'm giving talks about my recent statistical mechanics
research. The guest lecturers will teach Math 461 at the usual time and place. I will have office hours on Mondays as usual, but my office hours on Wednesday 3/6 and 3/13 are cancelled. Please feel free to email me questions.
I'm posting W/F lecture notes early these two weeks. Please turn in
HW as usual, i.e., in class or in my mailbox, both of which the guest
lecturer will take care of.
HW #7, due Friday Mar 15 by the end of class: Ch. 5: 6, 10, 12, 13, 15, 18, 22, 23, 25, 28, 32, 33.
Answers
HW #8 due Friday Mar 29 by the end of class: Ch. 5: 37, 38, 40, 41. Ch 6: 2, 7, 8, 9, 10.
Answers
Midterm 2, on April 5, covers homework problems up through and
including HW #8 and lectures through Apr. 1. This midterm is
comprehensive but emphasizes material not covered on Midterm 1. No HW
due on the day of the midterm. Practice midterm here.
Also, summary sheest for
discrete
distributions, their pmfs,
expectations, variances, and applications (of which you are responsible for
Geometric, Negative Binomial, and to a lesser extent Hypergeometric on
Midterm 2), and continuous
distributions, their pdfs, expectations, variances, and applications
(of which you are less responsible for Gamma and Cauchy on Midterm
2). Here's the distribution
table that will be on the midterm. The same table is here: https://twitter.com/kay314159/status/1113477572627771392
For logging in to see your scores, click the Score Reports link at https://math.illinois.edu/academics/courses/spring-2019-course-webpages.
HW #9 due Friday, April 12 by the end of class: Ch. 6: 14, 20, 21, 22,
23, 27, 29, 33. Also, the last problem from Midterm 2: what is the
pdf of X^2 if X is exponential with rate 4? Hint: compute the cdf of
Z = X^2 by setting up P(X^2 < = a) and using algebra inside the
parentheses to get an expression with X alone. Then use the pdf of
exponential in the correct integral, paying careful attention to the
bounds. Please do not turn in HW to my office; instead turn it in to
my mailbox, and if you're turning it in at 11am, please put it into the mailbox of Peixue Wu (for section B13) or Shufan Mao (for C13).
HW #10 due Friday April 19 by the end of class: Ch. 6: 38, 40, 41, 42,
48, and Ch. 7: 5, 6, 7, 8, 11.
Annoucement: There is no class on Monday, April 22, and no office hour.
HW #11 due Friday April 26 by the end of class: Ch. 7: 19, 21, 30, 31, 33, 38, 39, 41, 50, 51, 56.
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.
Emergency
information
Classmate contact info:
Schedule for lectures (lecture notes to be posted here)
Week 1: Introduction, sections 2.2-2.4 (including Chapter 1 as needed)
Wk 1
Monday lecture notes, Wk 1 Wednesday lecture notes, Wk 1
Friday lecture notes.
Week 2: Sections 2.4-2.5, 3.2 (including Chapter 1 as needed) Wk 2 Wednesday lecture notes, Wk 2
Friday lecture notes.
Week 3: Sections 3.3-3.4 (including Chapter 1 as needed) Wk 3
Monday lecture notes, No class, Wk 3
Friday lecture notes.
Week 4: Sections 4.1, 4.2, 4.10, 4.3 Wk 4
Monday lecture notes, Wk 4 Wednesday lecture notes, Wk 4
Friday lecture notes.
Week 5: Sections 4.3-4.6 Wk 5
Monday lecture notes, Wk 5 Wednesday lecture notes, Wk 5
Friday lecture notes.
Week 6: Sections 4.7-4.9, review, Wk 6
Monday lecture notes, Wk 6 Wednesday lecture notes, Midterm 1 on February 22
Week 7: Sections 5.1-5.3, Wk 7
Monday lecture notes, Wk 7 Wednesday lecture notes, Wk 7
Friday lecture notes.
Week 8: Sections 5.4-5.7, Wk 8
Monday lecture notes, Wk 8 Wednesday lecture notes, Wk 8
Friday lecture notes.
Week 9: Sections 5.7, 6.1, Wk 9
Monday lecture notes, Wk 9 Wednesday lecture notes, Wk 9
Friday lecture notes.
Week 10: (Spring break--no class)
Week 11: Sections 6.2-6.5, Wk 11
Monday lecture notes, Wk 11 Wednesday lecture notes, Wk 11
Friday lecture notes.
Week 12: Section 6.5-6.6, review, Midterm 2 on April 5 Wk 12
Monday lecture notes, Wk 12 Wednesday lecture notes.
Week 13: Sections 7.2-7.3, 7.7, 7.4 Wk 13
Monday lecture notes, Wk 13 Wednesday lecture notes, Wk 13
Friday lecture notes.
Week 14: Sections 7.4-7.7 Wk 14
Monday lecture notes, Wk 14 Wednesday lecture notes, Wk 14
Friday lecture notes.
Week 15: Sections 8.2-8.3 (No class Monday.) Wk 15 Wednesday lecture notes, Wk 15
Friday lecture notes.
Week 16: Section 8.2-8.3, review (last day of class: May 3) Wk 16
Monday lecture notes, No lecture notes for the review.
In place of answers to the old practice final, I'm going to post here another
practice final, 2012's, and at https://faculty.math.illinois.edu/~kkirkpat/finalPrime-Solutions.pdf.
FAQ1: If two RVs have the same mean and the same pdf/pmf, then does it
mean that the RVs are exactly the same?
Answer 1: In this situation, the two RVs have the same
distribution, and thus they are the same up to a set of probability
zero. We say that they are equal in law/distribution. (There's also
the difference between the RVs and their realizations that should be
taken into account.)
FAQ2: What is wrong with “Corr(X,Y)=0 if and only if X&Y are independent”?
Ans2: This makes sense but it's false. We did a CX to the FAQ2 statement
statement during a lecture.
FAQ3: What does CX mean?
Ans3: It’s short for “counterexample.”
FAQ4:
Ans4: