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.