### Math 425: Introduction to Probability

Fall 2006, Sections 7 and 8

Course meets:
Section 7: Tuesday and Thursday 10:10-11:30 in 330 Dennison.
Section 8: Tuesday and Thursday 2:40-4:00 in 1084 East Hall.

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

Office hours: Tuesday 1:10-2:30 and Thursday 5:10-6:30 in 2858 East Hall

Course homepage: http://www.math.lsa.umich.edu/~fomin/425f06.html

Text (required): Sheldon Ross, A First Course in Probability. 6th edition, Prentice-Hall, 2002.
IMPORTANT: Do NOT buy the latest 7th edition (dated 2006). It can be used as a textbook (the changes are minor), but it is more expensive.

Text differences: In the first 8 chapters all section numbers of the two editions are the same, except the 7th edition adds a new section 7.3, so that section 7.x in 6th edition corresponds to section 7.(x+1) in 7-th edition, for x between 3 and 8.

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, 25% each; 20% homework; 30% final exam (comprehensive).
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.

HW#1, due 9/12: Chapter 1, problems 3, 8(c), 12(a), 15, 22, 24, 26, 28, 30.
HW#2, due 9/19: Chapter 2, 12(a), 17, 21(b), 29(a), 32, 42, 43(b), 45, 47.
HW#3, due 9/26: Chapter 3, 4, 12, 14(a), 19, 24, 32, 43, 49. [Renumbered in 7th edition as 4, 16, 18(a), 13, 26, 36, 47, 53.]
HW#4, due 10/03: Chapter 3, 35, 44, 52, 58, 59(c), 62, 66, 67. [Renumbered in 7th edition as 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. Extra problems (not to be graded): 32, 33.
HW#8, due 11/21: Chapter 6, 6, 8, 14, 27(a), 32(a), 33(a), 34(a).
HW#9, due 12/5: Chapter 6, 42(a), 57; Chapter 7, 9(a), 12(b), 16, 19(a), 34, 39, 42 (1st part)
HW#10, due 12/12: Chapter 7, 51; Chapter 8, 2(b), 7, 12, 13(a), 15.

(Unless stated otherwise, problem numbers are the same in the 6th and 7th editions.)

Exams

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).

Past exams can be found on Dan Burns' webpage.

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

Exam #1 covers Chapters 1-3.

Exam #2 covers Chapters 4-5, with the exception of Sections 4.8.3-4.8.4, 4.9.2-4.9.4, 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

Final exam covers the topics covered by the midterm exams (see above), plus Sections 6.1-6.5, 6.7, 7.1-7.2 (except 7.2.1-7.2.2), 7.3-7.4 (except 7.4.2-7.4.4), 8.1-8.3, and 9.1.

Exam times

All exams will be held in the same room where the class meets.
First midterm: October 5.
Second midterm: November 7.
Times of the final exams, as determined by the Office of the Registrar:
Section 7: Tuesday, December 19, 1:30 pm - 3:30 pm, in 330 Dennison.
Section 8: Thursday, December 21, 4:00 pm - 6:00 pm, in 1084 East Hall.
Review sessions:
Section 7: Monday, December 18, 2 pm, in 4088 East Hall.
Section 8: Wednesday, December 20, 2 pm, in 4088 East Hall.