Math 5010-1: Introduction to Probability

Math 5010-1: Introduction to Probability. Fall 2013

Schedule: Meets 9:40--10:30 MWF, 8/26 to 12/13 except for 9/2, 10/14,16,18 and 11/29, in LCB 215. PhD students may want to register under the number 6805.

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

Instructor office hours: 2:00--2:50 MWF, JWB 119. Other times are available by appointment.

Teaching assistant: Because of the large size of the class, we have been assigned a teaching assistant. His name is Sung Chan Choi, and his email is imsanean@hotmail.com.

TA office hours: You can see Mr. Choi at the Tutoring Center (lower level, between JWB and LCB). His times are Tues., Thurs. 9am--12, and Wed. 6pm--8. We have been informed that Mr. Choi is a grader, not a TA, so he will grade assignments but will not have office hours. Sorry for the confusion.

Prerequisite: Math 2210 or 2520. (Basically, you'll need Calculus I, II, III.)

Text: We will use the text A First Course in Probability by Ross. Available for $104.89 at Amazon.com. Also available for $170.70 at U. Campus Store. It is not essential to have the latest (9th) edition. The 7th or 8th editions are sufficient.

Tentative syllabus: We'll try to cover Chapters 1--8.

Grades: Based on weekly homework (20%), two midterm exams at about 6 and 12 weeks (25% each), and a final exam (30%). The first midterm will cover Chapters 1--3, the second Chapters 4--6. The final exam, covering Chapters 1--8, is scheduled for Wednesday, December 18 at 8:00 a.m. Early exams are never given. Typically, 85--100 is an A, 70--85 is a B, 55--70 is a C, and so on, though these numbers are slightly flexible. Borderline cases will get a plus or minus.

Homework: Assigned problems will be posted on this webpage on Fridays. Solutions will be due the following Friday, except when stated otherwise. Hard copies are preferred, but homework can be emailed in emergency situations such as illness. (In that case, scan and send as a pdf file. If you use a word processor, convert to pdf before sending.) Late assignments cannot be accepted, but you can miss two assignments without penalty. The reason for the homework assignments is that this is the best way to learn this subject. If you choose to copy someone else's answers, it will not affect your homework score but it will likely affect your score on the next exam.

Exams: Exams can be made up if there is a very good justification and if arrangements are made in advance, but this is rare. (Phone the department office before the exam begins to give notification if the instructor is not available; 581-6851.)

Expected learning outcomes: The student who successfully completes the course will be conversant with the basics of probability, including such topics as combinatorial analysis, random variables, distributions, independence, conditional probability, expected value and moments, the law of large numbers, and the central limit theorem. This will provide enough preparation for Math 5080 (statistical inference), Math 5040 (stochastic processes), Math 5030 (actuarial mathematics), and Math 5760 (mathematical finance).

Week 1: Aug. 26, 28, 30. We covered Chapter 1 through multinomial coefficients. Assignment 1: Chapter 1, Problems 3, 5, 7, 8, 13, 15, 17, 18, 20, 21. (Sorry for the delay, but it took some time to confirm that the ten problems are identical in Editions 7, 8, and 9. So it doesn't matter which edition you use.)
Week 2: Sep. 4, 6. We finished Chapter 1 and started Chapter 2, getting through Section 2.2. Assignment 2: Chapter 1, Problems 24, 26, 27, 28, 31, 32; Chapter 2, Problems 2, 3, 4, 6.
Week 3: Sep. 9, 11, 13. We nearly finished Section 2.5. Assignment 3: Chapter 2, Problems 11, 13, 15(b), 25, 33, 34, 36, 48, 50, 55.
Week 4: Sep. 16, 18, 20. We covered through the conditioning law, i.e., (3.1) and (3.4), but have not yet covered Bayes's law. Assignment 4: Chapter 3, Problems 1, 3, 5, 6, 7, 8, 11, 13, 14, 41.
Week 5: Sep. 23, 25, 27. We nearly finished Chapter 3. Assignment 5: Chapter 3, Problems 20, 23, 26, 36, 43, 51, 60, 73, 78, 79.
Week 6: Sep. 30, Oct. 2, 4. We covered through the definition of expectation. No new assignment this week, except to prepare for midterm exam 1.
Week 7: Oct. 7, 9, 11. We had Exam 1. Solutions. We covered through the binomial and geometric distributions in Chapter 4. Assignment 6: Chapter 4, Problems 4, 7, 11(a), 15, 19, 21, 23, 32, 46, 49. (Due Oct. 25.)
Week 8: Oct. 21, 23, 25. We finished Chapter 4 and started continuous random variables, getting through Section 5.2. Assignment 7: Chapter 4, Problems 52, 61, 72, 78, 80(a); Chapter 5, Problems 1, 4, 5, 6, 7.
Week 9: Oct. 28, 30, Nov. 1. We covered Chapter 5 through the exponential distribution. Assignment 8: Chapter 5, Problems 10, 11, 13, 15, 16, 21, 23, 27, 32, 34.
Week 10: Nov. 4, 6, 8. We finished Chapter 5 and started Chapter 6, nearly finishing Section 6.2. Assignment 9: Chapter 5, Problems 37, 38, 40; Chapter 6, Problems 1a,b, 2, 7, 8a,b, 10, 15, 22.
Week 11: Nov. 11, 13, 15. We finished Chapter 6, omitting Sections 6.6--6.8. Assignment 10: Chapter 6, Problems 18, 19, 23, 24, 28, 30, 38, 40, 42, 43.
Week 12: Nov. 18, 20, 22. We got through Section 7.4 (skipping Section 7.3). No new assignment this week, except to prepare for midterm exam 2 on Monday.
Week 13: Nov. 25, 27. We had Exam 2. Solutions. We finished Section 7.5.1. Assignment 11 (for Dec. 6): Chapter 7, Problems 4, 5, 8, 13, 21, 22, 25, 38, 41, 45.
Week 14: Dec. 2, 4, 6. We finished Chapter 7, skipping Sections 7.3, 7.6, 7.8, and 7.9, and we started Chapter 8. Assignment 12 (last one): Chapter 7, Problems 51, 53, 55, 63, 75, 78ab. Chapter 8, Problems 2, 4, 6, 13. (These last four problems may require material that will be covered next week.)
Week 15: Dec. 9, 11, 13. We finished Chapter 8 through the central limit theorem.

Note: Final exam is scheduled for Wednesday, Dec. 18, 8:00--10:00 am. You may bring one 8.5x11 sheet of notes/formulas (two-sided). Calculators are OK. Old exam for practice: 2005 Final. ~~(Solutions are not available.)~~ Answers.