Math 351: Probability (Fall 2018)

3:00pm - 4:15pm, Tuesday/Thursday

Instructor: Daniel M. Anderson (4411 Exploratory Hall, 703.993.1482,
Office Hours: Tuesday 6:30PM-7:30PM, Thursday 1:30PM-2:30PM, and by appointment.

Text: A First Course in Probability, Ninth Edition, by Sheldon Ross.

Prerequisites: A grade of C or better Math 213 (Calculus III) or equivalent.

Course Goals: To understand and be able to make use of the concepts of random variables, probability functions, special distributions, and limit theorems.

Exams: There will be two midterm exams. Midterm exam dates and topics listed below are tentative and will be confirmed in class. You are responsible for being aware of any such changes announced in class. Makeup exams will not be given. In the event that one exam is missed and (1) a valid, documented excuse is given in writing to the instructor at the time of the absence and (2) the student provides sufficient evidence to the instructor that he/she is keeping up with the topics in the course, the final exam score will count in place of the missed exam. The instructor will determine whether an excuse is valid (for example, a medical emergency would constitute a valid excuse but leaving early for vacation is not a valid excuse). Without a valid documented excuse given at the time of the exam, a missed exam will count as a zero. If more than one midterm exam is missed, that situation will be dealt with on an individual basis.

Graded Homework: There will be regularly assigned homework problems.

Resources: A group of students and faculty at MIT have compiled a solutions to the problems listed in the seventh edition of Ross. You can find these at the following webpage.

Grading Policy:
Homework = 20%
Midterm Exams = 25% each
Final Exam = 30%

In general, 90%-100% = A, 80%-89% = B, 70%-79% = C, 60%-69% = D, below 60% = F. Plus and minus grades will be approximately 2 or 3 percentage points above or below these boundaries (e.g. 88% would correspond to a B+). I reserve the right to lower the curve, but will not raise the curve.

Topics Covered/Schedule
Chapter 1: Combinatorial Analysis
Chapter 2: Axioms of Probability
Chapter 3: Conditional Probability and Independence
EXAM 1 Chapters 1-3 (Thursday, September 27)
Chapter 4: Random Variables
Chapter 5: Continuous Random Variables
Chapter 6: Jointly Distributed Random Variables
EXAM 2 Chapters 1-5 (Thursday, November 8)
Chapter 7: Properties of Expectations
Chapter 8: Limit Theorems
FINAL EXAM Chapters 1-5 (Thursday, December 13, 1:30-4:15pm)

Final Exam: The final exam will be an in-class exam and must be taken at the scheduled time. Exceptions are allowed only with a Dean's permission, by University rules.

Calculators/Phones/Etc.: Calculators, smartphones, ipads, laptops, etc. will not be allowed for use during exams. Plan to turn off and put away all mobile electronic devices during exams -- accessing these devices between the time you receive your exam and the time you turn in your exam constitutes an honor code violation.

Honor System: THIS IS IMPORTANT. PAY ATTENTION TO THIS. It is expected that each student in this class will conduct himself or herself within the guidelines of the Honor Code. All academic work should be done with the level of honesty and integrity that this University demands. Anyone caught cheating during an exam or on any other material submitted for grade will be sent to the University Honor Committee for formal resolution to the situation.The use of cell phones and other electronic communication devices for any purpose during an exam will be considered an honor code violation. The most likely recommendation given by the professor to the Honor Committee is failure of the class (not just the specific exam, etc.) if the student is found guilty of violating the Honor Code.

General Information for using computers at GMU [including setting up Mason account]

Lecture Topics: (section numbers based on A First Course in Probability, 9th Edition, by Sheldon Ross)
Tuesday, August 28: 1.1-1.4 [Practice Problems: Ch 1: 1,2,3,8,9,14,18,20,25,26,30] [Lecture Notes for Chapter 1 (8/28/2018 and 8/30/2018)]
Thursday, August 30: 1.4-1.5 [Homework 1 (Due, Thursday, September 6)],[Homework 1 Solutions]
Tuesday, September 4: 2.1-2.3 [Practice Problems: Ch 2: ('Problems' starting on p. 48): 1,2,4,8,12,13,15,16,17,25,27,36, ('Theoretical Exercises' starting on p. 52): 6]
Thursday, September 6: 2.4,2.5 [Lecture Notes for Chapter 2 (9/4/2018, 9/6/2018, 9/11/2018, 9/13/2018)]
Tuesday, September 11: Ch. 2 [Homework 2 (Due, Tuesday, September 18)],[Homework 2 Solutions]
Thursday, September 13: Ch. 2, 3.1,3.2 [Practice Problems: Ch 3: ('Problems' starting on p. 97): 3.1,3.5,3.6,3.9,3.10,3.11,3.14,3.18,3.23,3.24,3.26,3.37,3.45,3.48,3.84 ('Theoretical Exercises' starting on p. 106): 3.4]
Tuesday, September 18: 3.1, 3.2 [Lecture Notes],[Homework 3 (Due, Tuesday, September 25)]
Thursday, September 20: 3.3,3.4 [Lecture Notes]
Tuesday, September 25: 3.3 [Lecture Notes],[Homework 3 Solutions]
Thursday, September 27: EXAM 1 (Ch. 1-3)
Tuesday, October 2: 3.4,4.1 [Lecture Notes]
Thursday, October 4: 4.1,4.2,4.3,4.4 [Lecture Notes], [Practice Problems: Ch 4: ('Problems' starting on p. 163): 4.1,4.2,4.4,4.9,4.17,4.19,4.40,4.43,4.56,4.71,4.72,4.75,4.78]
Tuesday, October 9: Fall Break (Monday classes meet Tuesday, No Tuesday Classes)
Thursday, October 11: 4.2,4.3,4.4 [Lecture Notes],[Homework 4 (Due, Tuesday, October 23)],[Homework 4 Solutions]
Tuesday, October 16: 4.4,4.5 [Lecture Notes]
Thursday, October 18: 4.6-4.8 [Lecture Notes]
Tuesday, October 23: 4.9,5.1 [Lecture Notes]
Thursday, October 25: 5.1,5.2 [Lecture Notes], [Practice Problems: Ch 5: ('Problems' starting on p. 212): 5.1-5.5,5.7,5.8,5.11,5.14,5.15]
Tuesday, October 30: 5.2,5.3,5.4 [Lecture Notes],[Homework 5 (Due, Tuesday, November 6)],[Homework 5 Solutions (problems 3-6)] [Additional Practice Problems: Ch 5: ('Problems' starting on p. 212): 5.21,5.26,5.27,5.28,5.32,5.34, ('Theoretical Exercises' starting on page 214): 5.9, 5.13,5.14]
Thursday, November 1: 5.3,5.4 [Lecture Notes]
Tuesday, November 6: Ch.5 [Lecture Notes]
Thursday, November 8: EXAM 2 (Ch 1-5)
Tuesday, November 13: 5.5,5.6 [Lecture Notes]
Thursday, November 15: 6.1,6.2
Tuesday, November 20: 6.3,6.4
Thursday, November 22: THANKSGIVING
Tuesday, November 27: 7.1,7.2,7.3
Thursday, November 29: 7.4,7.5
Tuesday, December 4: Ch. 8
Thursday, December 6: Ch. 8
FINAL EXAM: Thursday, December 13, 1:30-4:15pm

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