### Math 425: Introduction to Probability

Fall 2016, Sections 5 and 9

Course meets:
Section 5: Monday, Wednesday, and Friday 1:10-2:00 in 1084 East Hall.
Section 9: Monday, Wednesday, and Friday 12:10-1:00 in 1084 East Hall.

Instructor: Sergey Fomin, 4868 East Hall, fomin@umich.edu

Office hours: Monday 2:10-3:00 and Wednesday 2:10-4:00 in 4868 East Hall.

Course homepage: http://www.math.lsa.umich.edu/~fomin/425f16.html

Text (required): Sheldon Ross, A First Course in Probability, 9th edition, Prentice-Hall, 2014.

Where can I buy this textbook? (compare to publisher's online store; also check out international editions)

Prerequisites: Math 215 or 285 (Multi-variable calculus).

Course synopsis:
This course introduces students to the theory of probability and to a number of applications. Topics include the basic results and methods of both discrete and continuous probability theory: conditional probability, independent events, random variables, jointly distributed random variables, expectations, variances, covariances. The material corresponds to most of Chapters 1-7 and part of 8 of Ross.

Grade will be based on homework (20%) and three exams (80%), see below. This course will not be graded on a curve, i.e., there are not a set number of each grade to be given out. Every student with the total score of 90% (resp., 80%, 70%, 60%) is guaranteed the final grade of A (resp., B or higher, C or higher, D or higher).

Exams

• First exam (30% of the grade): Thursday, October 6, 6:10-7:30 pm, 1360 East Hall.
• Second exam (30% of the grade): Monday, November 7, 7:10-8:30 pm, 296 Weiser Hall.
• Third exam (20% of the grade): Monday, December 12, regular class time and location.

Exams are closed book, closed notebook. No electronic devices are allowed except calculators. You are allowed to bring a 3-by-5 index card to the 1st exam, two such cards to the 2nd exam, and three cards to the 3rd one.

Past exams can be found on Math 425 pages by Dan Burns and Hugh Montgomery.

Exam #1 covers Chapters 1-3. Practice problems for Exam #1 and answers to them.

Exam #2 covers Chapters 4-5, with the exception of Sections 4.8.3-4.8.4, 5.5.1, 5.6.
Practice problems for Exam #2: Self-Test Problems and Exercises in Chapter 4: 3, 13, 15; and in Chapter 5: 11, 12.

Exam #3 covers Sections 6.1-6.5, 6.7, 7.1-7.2 (except 7.2.1-7.2.2), 7.4, 7.5.1, and 8.1-8.3.
Practice problems for Exam #3: Self-Test Problems and Exercises in Chapter 6: 7, 15; Chapter 7: 13; and in Chapter 8: 10.

Homework

• There will be approximately 10 problem sets.
• Your lowest homework set score will be dropped.
• No late homework will be accepted.
• In each homework assignment, 5 problems will be graded.
• All answers should be justified by a sound argument. An answer lacking justification will receive no credit.
• Collaboration on the homework is allowed, but all collaborators must be acknowledged by name, and each person is responsible for writing up her/his own solutions.

HW#1, due 9/14  9/16: Chapter 1, problems 3, 8(c), 12(a), 15, 22, 24, 26, 28, 30.
HW#2, due 9/21: Chapter 2, 12(a), 17, 21(b), 29(a), 32, 42, 43(b), 45, 47.
HW#3, due 9/28: Chapter 3, 4, 13, 16, 18(a), 26, 36, 47, 53.
HW#4, due 10/05: Chapter 3, 39, 48, 56, 62, 63(c), 66, 70, 71.
HW#5, due 10/19: Chapter 4, 4, 14, 22(b), 32, 38, 41, 43, 48.
HW#6, due 10/26: Chapter 4, 54, 64(b), 65(b); Chapter 5, 1, 5, 7, 11, 13(b).
HW#7, due 11/2: Chapter 5, 18, 19, 21, 24, 27, 32, 33.
HW#8, due 11/16: Chapter 6, 6, 8, 14, 27, 29(a), 30(a), 31(a).
HW#9, due 11/30: Chapter 6, 41(a), 58; Chapter 7, 9(a), 12, 19(a), 34(a).
HW#10, due 12/7: Chapter 7, 34(b), 39, 42 (1st part), 51; Chapter 8, 7, 13(a), 15.