## Math 20: Discrete Probability

67
If you play a Game of Chance, know, before you begin,
If you are benevolent you will never win.

-- William Blake, EPIGRAMS, VERSES, AND FRAGMENTS FROM THE NOTE-BOOK

Announcements and Assignments

• Study for the Final: 1.2, 3.1, 3.2, 4.1, 5.1, 6.1, 6.2, 8.1, 9.1, 9.2, 11.1, 11.2, 11.3.
• Homework 9 (not to be handed in): 11.3) 1, 2, 3, 4, 5, 7, 8, 9, 12.
• Homework 8 (due on Nov. 23): 11.1) 7, 8, 19; 11.2) 3, 4 (Also find Nc and NR and interpret the results), 8, 15, 34. Practice Problems: 11.1) 1, 3, 5, 11, 12; 11.2) 9, 10, 19, 24.
• Homework 7 (due on Nov. 16): 9.1) 2, 4 (do this problem only for S between 499,500 and 500,500), 6, 12; 9.2) 1, 2, 11. Practice Problems: 9.1) 3, 10, 14; 9.2) 5, 6, 7.

• Proof of Central Limit Theorem for Binomial Distribution

• Study for Exam 2: 1.2, 3.1, 3.2, 4.1, 5.1, 6.1, 6.2.
• Homework 6 (due on Nov. 9): 8.1) 8, 10, 12. Practice Problems: 8.1) 9, 11.

• Homework 5 (due on Nov. 2): 6.1) 6, 8, 13, 16, 18; 4.1) 47, 49; 6.2) 12, 14, 15. Practice Problems: 6.1) 12, 17, 20, 35; 4.1) 39; 6.2) 9, 10, 11, 20, 21.

• Homework 4 (due on Oct. 26): 5.1) 14, 16, 18, 33, 35. Practice Problems: 5.1) 10, 20, 22, 28, 40, 42.

• No homework due on Oct. 19. Study for Exam 1: 1.2, 3.1, 3.2, 4.1.

• Homework 3: 4.1) 13, 15, 17, 22, 23, 24. Read Example 4.6. Practice Problems: 4.1) 3, 9, 14, 16, 19, 26, 27.

• Here is an interesting website: Virtual Laboratories in Probability and Statistics.
• Homework 2: 3.1) 6, 7, 10, 12; 3.2) 9, 10, 12, 13, 17. Read "Choosing a Sample Space" on pages 106 and 107.
Practice problems (not to be handed in): 3.1) 8, 13, 14, 15; 3.2) 1, 8, 19, 20.

• Please note that the office hours for Mondays has changed from 3-4 to 12-1.
• Homework 1: 1.2) 6, 7, 9, 18, 19. Practice problems (not to be handed in): 1.2) 1, 4, 5, 14, 17a, 17b.
• Here is an interesting website: RANDOM.ORG.
• There will be no office hours on Friday, Oct. 2. Instead, I will hold an office hour on Tuesday, Oct. 6 from 2 to 3.

• There will be no class on Monday, Oct. 5. Instead, we will use the x-hour on Thursday, Oct. 8. Homework 2 will be due before the class starts on Wednesday, Oct. 7.

• General Information

Textbook

Introduction to Probability (Second Revised Edition) by Charles M. Grinstead and J. Laurie Snell
This book is available at Wheelock Books and also may be downloaded from here.

Scheduled Lectures

 M-W-F 1:45 - 2:50 X-hour: Th 1:00 - 1:50 Kemeny 108

Instructor

 Amir Barghi Office: 216 Kemeny Hall Office Hours: M 12-1 W & F 3:00 - 4:00 and by appointment. BlitzMail: [firstname] {dot} [lastname]

Exams

There will be 2 midterms and a final exam.

 Exam 1 Oct. 19, 5-7 Kemeny 108 Exam 2 Nov. 9, 5-7 Kemeny 108 Final Exam Dec. 6, 3-6 Kemeny 105

Homework Policy

• Homework will be assigned weekly and will be due at the beginning of class on Mondays. Homework should be written neatly and stapled.
• Late homework will not be accepted. Permission for a late homework is granted under one and only one circumstance: an illness. In case of an illness, a student must provide the instructor with a note from the Dick's House.

 Class Participation 5% Homework 20% Exam 1 20% Exam 2 20% Final Exam 35%

The Honor Principle

• On Exams: No help is given or received. Written notes, calculators, and computers are not permitted.
• On Homework: Collaboration on homework is permitted and encouraged; however, it is a violation of the honor code for one student to provide an answer or a proof for another student. In other words, a student should feel free to talk to other students while thinking about a problem, but every student should write up her/his individual solutions independently. In case of any questions in this regard, please e-mail the instructor or ask during office hours.

Disabilities

Students with learning, physical, or psychiatric disabilities enrolled in this course who may need disability-related classroom accommodations are encouraged to make an appointment to see me before the end of the second week of the term. All discussions will remain confidential, although the Student Accessibility Services office may be consulted to discuss appropriate implementation of any accommodation requested. At such a meeting please provide me with a copy of a completed "Accommodations/Consent" form, which lists the accommodations recommended for the student by Student Accessibility Services. If you do not have such a form, please visit the Student Accessibility Services office at Collis 301.

Religious Observances

Students who have conflicts with the course or the exam schedule due to religious observances should make arrangements with the instructor as soon as possible (before the end of the second week).

Syllabus

The following is a tentative syllabus for the course.

Week Sections in Text Brief Description
1 1.2, 3.1 Basic Probability, Combinatorics and Permutations
2 3.2, 4.1 Combinations and Conditional Probability
3 6.1, 6.2 Expected Value and Variance
4 5.1 Important Distributions ~~ Exam 1, Oct. 19 @ 5
5 8.1 Law of Large Numbers
6 9.1 Central Limit Theorem: Bernoulli Trials
7 9.2 Central Limit Theorem: Independent Trials ~~ Exam 2, Nov. 9 @ 5
8 11.1, 11.2 Introduction to Markov Chains, Absorbing Markov chains.
9 11.3 Regular Markov Chains, Ergodic Markov Chains
10 Review Review

Last updated on Sep. 28, 2009 by Amir Barghi