### Math 425: Introduction to Probability

Winter 2004, Sections 3 and 7

Course meets: Section 3: MWF 1-2 in 1084 East Hall; Section 7: MWF 2-3 in 1084 East Hall.

Instructor: Sergey Fomin, 2858 East Hall, 764-6297, fomin@umich.edu

Office hours: M 3-4 and Th 3-5 in 2866 or 2858 East Hall.

Course homepage: http://www.math.lsa.umich.edu/~fomin/425w04.html

Text (required): Sheldon Ross, A First Course in Probability, 6th edition, Prentice-Hall, 2002.

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

From departmental course description:
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 two 1-hour midterm exams, 20% each; 20% homework; 40% final exam.
Your lowest homework set score will be dropped.

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).

Homework: There will be approximately 10 problem sets.

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 fine, but each person is responsible for writing up her/his own solutions.

Exams are closed book, closed notebook. You will be allowed to bring a 3-by-5 index card to the 1st midterm, two such cards to the 2nd midterm, and three cards to the final. One problem on each midterm exam will be taken directly from homework (perhaps with altered numerical values).

The midterm exams are held in class. No makeups will be given.

Schedule
This syllabus is incomplete and tentative, and will be superseded by later versions as the course evolves.

 # date sections in Ross problems 1 1/7 1.1-1.3 2 1/9 1.4 3 1/12 1.5-1.6 4 1/14 2.1-2.2 HW#1 due Chapter 1, 3, 8(c), 12(a), 15, 22, 24, 26, 28, 30 5 1/16 2.3-2.4 6 1/21 2.5 7 1/23 2.5 HW#2 due Chapter 2, 12(a), 17, 21(b), 29(a), 32, 42, 43(b), 45, 47 8 1/26 3.1-3.2 9 1/28 3.3 10 1/30 3.4 HW#3 due Chapter 3, 4, 12, 14(a), 19, 24, 32, 43, 49 11 2/2 3.4 12 2/4 3.5 13 2/6 4.1 HW#4 due Chapter 3, 35, 44, 52, 58, 59(c), 62, 66, 67 14 2/9 Exam #1 covers Ch. 1-3 Practice problems for Exam #1 and answers to them 15 2/11 4.2, 4.9 16 2/13 4.3-4.5 17 2/16 4.6 18 2/18 4.6 19 2/20 4.7, 9.1 HW#5 due Chapter 4, 4, 14, 22(b), 32, 38, 41, 43, 48 winter vacation 20 3/1 5.1-5.2 21 3/3 5.3 22 3/5 5.4 HW#6 due Chapter 4, 54, 64(b), 65(b); Chapter 5, 1, 5, 7, 11, 13(b) 23 3/8 5.4.1 24 3/10 5.5 25 3/12 5.7 HW#7 due Chapter 5, 18, 19, 21, 24, 27, 32, 33 26 3/15 6.1 27 3/17 Exam #2 covers Ch. 4-5* Practice problems for Exam #2: Self-Test Problems and Exercises in Chapter 4, 3, 13, 15; and in Chapter 5, 11, 12 28 3/19 6.1 29 3/22 6.2 30 3/24 6.3 31 3/26 6.4-6.5, 7.4.1 32 3/29 6.7 HW#8 due Chapter 6, 6, 8, 14, 27(a), 32(a), 33(a), 34(a) 33 3/31 7.1-7.2 34 4/2 7.2 35 4/5 7.3 36 4/7 7.3 37 4/9 7.4 HW#9 due Chapter 6, 42(a), 57; Chapter 7, 9(a), 12, 16, 19(a), 32**, 39, 42 (1st part) 38 4/12 8.2 39 4/14 8.2 40 4/16 8.3 41 4/19 10.2-10.3 HW#10 due Chapter 7, 51; Chapter 8, 2(b), 7, 11, 13(a), 15. 42 4/21 Q&A session TBA Final exam TBA TBA Practice problems for the final exam Sample final exam (by J.Wolbert)

*except Sections 4.8.3-4.8.4, 4.9.2-4.9.4, 5.5.1, 5.6

**In problem 7.32, you may leave the answer as a single/double/triple sum.