Math 5010-2: Introduction to Probability

Math 5010-2: Introduction to Probability, Fall 2007

Schedule: Meets 6--9 pm Wednesdays, 8/22 to 12/12 except 10/10 (15 classes and a final exam), in LCB 215.

Notice: PhD students wishing to get credit for this course should register under the number 6805.

Instructor: S. Ethier (Prof.), 581-6148, ethier@math.utah.edu

Office hours: 11--12 MW and 4:30--5 W, JWB 119.

Prerequisite: Math 2210 or 2520. (Basically, you'll need calculus up through double integrals.)

Text: Elementary Probability, 2nd Ed., by David Stirzaker.

Grades: Based on weekly quizzes (20%), two midterm exams (25% each), and a final exam (30%). Typically, 85-100 is an A, 70-85 is a B, 55-70 is a C, and so on. Borderline cases will get a plus or minus.

Homework: Assigned problems will be posted on this webpage the day after we meet. Solutions will not be collected, but instead quizzes will require you to keep current.

Quizzes: There will be a 15-minute quiz most weeks based on the material covered the previous week. Make-ups are not given, but up to three absenses are permitted. If a quiz is turned in, it counts. Anyone absent more often than three times should not be taking the course.

Exams: There will be two midterm exams, the first based on Chapters 1-3, the second based on Chapters 4-6 or 4-7. Exams can be made up if there is a very good justification and if arrangements are made in advance. (Phone the department office to give notification if the instructor is not available; 581-6851.)

Tentative syllabus: We'll try to cover the first 8 chapters in the text, with lighter emphasis on Chapter 6. This will give you enough preparation for Math 5080 (mathematical statistics), Math 5040 (stochastic processes), and Math 5030 (actuarial mathematics).

Aug. 22 class. We covered most of the material in Chap. 1 and worked Example 1.13. Assignment for next week: Problems (on page 48++) 4, 6, 9, 10, 11, 12(b), 15, 19, 22, 23.
Aug. 29 class. We finished Chap. 1 and started Chap. 2, getting to about the middle of page 55. Assignment for next week: Problems (on page 76++) 1, 3, 5, 6, 7, 9, 20, 34, 35, 36.
Sept. 5 class. We finished Chap. 2. We worked Example 2.6 (Sol. I) and started Example 2.11. Assignment for next week: Problems (on page 78++) 12, 15, 19, 23, 24, 25, 27, 28, 41, 43.
Sept. 12 class. We started Chap. 3, getting through Theorem 2 on page 86, and we also covered the binomial and multinomial theorems. Assignment for next week: Problem 45 on page 82 and Problems 1--4, 6, and 9--11 on page 108++.
Sept. 19 class. We finished Chapter 3, though we didn't get into the complicated examples at the end of the chapter. Assignment for next week: Problems (on page 110++) 14, 15, 17, 19, 20, 21, 26, 27, 37, 44.
Sept. 26 class. We started Chap. 4, getting through about page 120. Assignment for next week (in addition to studying for exam): 1, 2, 5, 6, 7, 10, 13.
Oct. 3 class. Midterm exam was given. Also, we nearly finished Section 4.3. Assignment for next week (Oct. 17): Problems (on page 152++) 16, 18, 19, 24, 25, 29.
Oct. 17 class. We finished Chapter 4. Assignment for next week: Problems (on page 153++) 27, 30, 33, 35, 37, 39, 40, 42, 45.
Oct. 24 class. We got to the definition on page 170. Assignment for next week: Problems (on page 226++) 1, 2, 3, 6, 9, 10, 12, 14, 15.
Oct. 31 class. We covered through Section 5.5. We will omit Sections 5.6, 5.7, and 5.9. Assignment for next week: Problems (on page 228++): 18, 21, 23, 24, 31, 33, 35, 36, 40.
Nov. 7 class. We finished Chapter 5 and most of Chapter 6 (through Section 6.4, omitting a few topics such as Theorem 5 on page 234). Assignment for next week: Problems (on page 281++) 2a,c,e, 3, 6, 7, 10.
Nov. 14 class. We finished Chapter 6, omitting Sections 6.7 and 6.8, and we started Chapter 7, getting through Section 7.1. Assignment for next week: Problems (on page 282) 15--17 and (on page 334) 1--6.
Nov. 21 class. We nearly finished Chapter 7, omitting Sections 7.7--7.9. Assignment for next week: Problems (on page 334++) 7, 8, 10, 11, 23, 24, 26, 28.
Nov. 28 class. 2nd midterm exam was given. Also, we covered Section 8.1. Assignment for next week: Problems (on page p. 391++) 1, 3, 4, 5.
Dec. 5 class. We finished Chapter 8, omitting Sections 8.7 and 8.8, and with light coverage of Section 8.2. Last assignment: Problems (on page 391++) 2, 13, 19, 20, 32, 40, 44(i).

Final exam info: This will be held in the usual room (LCB 215) from 6 to 8 pm Wednesday, December 12. You may bring one formula sheet (2-sided) but may not exchange it with anyone else during the exam. Because scores were low on Exam 2, your score on the final will replace your score on Exam 2 if it is higher. Still, you will need to understand the material better to score significantly better. Therefore, I recommend that you focus on a subset of the assigned problems this semester and learn how to do them. Here is my suggested list:

Chap. 1: 4, 6, 10, 15.
Chap. 2: 1, 3, 5, 20, 27, 41.
Chap. 3: 3, 9, 11, 19.
Chap. 4: 1, 2, 25, 27, 29.
Chap. 5: 1, 2, 10, 12, 24, 31.
Chap. 6: 2, 6, 7, 15.
Chap. 7: 1, 7, 10, 23, 28.
Chap. 8: 1, 2, 13, 32, 44(i).

Practice Final Exam. Answers.