## Math-M463/S463 Introduction to Probability Theory

Section: 14385/14417
Class Day and Times: MWF 9:05 - 9:55 am
Class Location: SW 221
Text: Mathematical Statistics and Data Analysis by John Rice
WEB Page: http://elizabethhousworth.com/Fall2010/Math463
Instructor: Elizabeth Housworth
Office and Office Hours: 371 Rawles Hall, 11:10-11:45 MWF, 2-2:45 TuTh, and by appointment
Important dates: Last day for automatic withdrawals is Wednesday, October 27. The final exam for our section of Math 463 is 5-7 pm on Monday, December 13.

 Grading Procedure and class policies: Homework is due in class on the dates indicated on the syllabus below. If you know you will have to miss class, you may turn in your homework early. Late homework will not generally be accepted. In cases of dire illness or other emergencies, short delays in turning in the assignment may be allowed but proof of illness or emergency may be required as well. There is a participation component to the course grade to encourage attendance. There may be random group pop quizzes to give me a sense of your understanding of the material, to facilitate your learning, and to check attendance.
Points
Homeworks  100
Attendance and Participation    50
Exam 1  100
Exam 2  100
Final Exam  150
--------------------------------
Total  500

Cheating Policy: You can work together on the homeworks. Exams are individual work only and if I have determined that you have cheated, I will give you an F in the course.

Religious Holiday Policy: If you will miss class, especially a class during which there will be an exam or other required work, for a religious holiday, you must inform me during the first two weeks of the semester.

Tentative Syllabus
Date Topics Work Due
Monday, August 30 1.1-1.3: Sample spaces and probability measures --
Wednesday, September 1 1.4: Combinatorics --
Friday, September 3 1.4: Combinatorics --
Monday, September 6 1.4: Combinatorics --
Wednesday, September 8 1.5: Conditional probabilities and Bayes's Theorem --
Friday, September 10 1.6: Independence Chapter 1: 5, 7, 13, 18, 23, 24, 28, 33, 34, 35.
Monday, September 13 2.1: Models for discrete data --
Wednesday, September 15 2.2: Models for continuous data --
Friday, September 17 2.2: Models for continuous data Chapter 1: 39, 47, 53, 56, 57, 68, 70, 74, 75, 78.
Monday, September 20 2.3: Functions of a random variable --
Wednesday, September 22 2.3: Functions of a random variable --
Friday, September 24 Catch-up day/problem session/review Chapter 2: 8, 9, 10, 11, 14, 16, 21, 24, 27, 32.

Tentative Syllabus
Date Topics Work Due
Monday, September 27 3.2: Joint distributions of discrete random variables --
Wednesday, September 29 3.3 Joint distributions of continuous random variables --
Friday, October 1 3.3 Joint distributions of continuous random variables Chapter 2: 34, 37, 42, 43, 44, 47, 49, 60, 67, 68. Extra credit: 72.
Monday, October 4 3.4: Joint distribution of independent random variables --
Wednesday, October 6 Review Practice Exam 1A
Practice Exam 1B
Friday, October 8 Exam 1 (covering chapters 1 and 2) --
Monday, October 11 3.5: Conditional distributions --
Wednesday, October 13 3.5: Conditional distributions --
Friday, October 15 3.6: Functions of jointly distributed random variables --
Monday, October 18 3.6: Functions of jointly distributed random variables --
Wednesday, October 20 3.6: Functions of jointly distributed random variables --
Friday, October 22 3.7: Extrema and order statistics Chapter 3: 2, 5, 6, 11, 23, 24, 27, 28, 29, 30.
Monday, October 25 4.1: Expected values --
Wednesday, October 27 4.1: Expected values --
Friday, October 29 4.2: Variance and standard deviation Chapter 3: 32, 38, 43, 44, 47, 55, 64, 67, 70, 74.
Monday, November 1 4.3: Covariance and correlation --
Wednesday, November 3 4.3: Covariance and correlation --
Friday, November 5 4.4: Conditional expectation and prediction Chapter 4: 8, 9, 10, 11, 13, 15, 18, 36, 37, 42.
Monday, November 8 4.4: Conditional expectation and prediction --
Wednesday, November 10 4.5: Moment generating functions --
Friday, November 12 4.6: Approximate methods --
Monday, November 15 Review --
Wednesday, November 17 Review Practice Exam 2A
Practice Exam 2B
Friday, November 19 Exam 2 (covering material through 4.2) --

Tentative Syllabus
Date Topics Work Due
Monday, November 22 Approximate Methods --
Wednesday, November 24 Thanksgiving Break --
Friday, November 26 Thanksgiving Break --
Monday, November 29 5.2: Law of Large Numbers Chapter 4: 49, 52, 53, 68, 83, 75, 77, 84, 85, 102. Can be turned in on Wednesday.
Wednesday, December 1 5.3: Convergence in distribution Exam 2 re-write due. If you made less than 80% on Exam 2, re-write the ENTIRE exam and turn it in during class today.
Friday, December 3 5.3: The Central Limit Theorem --
Monday, December 6 Chapter 6: The distribution of common sample statistics --
Wednesday, December 8 Catch up day/review/evaluations Chapter 5: 1, 2, 6, 7, 11, 12, 16, 20 (skip the part about comparing to part (a) of previous problems), 28, 29.
Friday, December 10 Review/evaluations Practice Final Exam A
Practice Final Exam B
Final - Monday, December 13, 5-7 pm