Download Math 3081 Probability and Statistics Spring 2016

Math 3081
Probability and Statistics
Spring 2016
Instructor: Hanai Sadaka
Office: 543 NI
Phone: 617-373-4882 (Math Dept. Office: 373-2450)
Email: [email protected]
Office Hours: Mondays and Wednesdays: 2:45-4:15 or by appointment
Text: “An Introduction to Mathematical Statistics and its Applications”, R. Larsen and M. Marx, fifth edition. (Published
by Prentice Hall).
Grading: Quizzes --- 20%; Two in-class exams --- 40%; Final Exam --- 40%
93-100 A
90-92 A87-89 B+
83-86 B 80-82 B73-76 C
70-72 C67-69 D+
63-66 D 60-62 D
77-79 C+
0-59 F
There will be 4 quizzes, two 1 hour tests and a final exam. The final will be cumulative. Borderline grades are determined
by the final exam score. One lowest quiz score is dropped.
This is an introduction course to the theory of probability and statistics. Its goal is to develop the mathematical tools and
concepts necessary for modeling uncertainty and data analysis in real-world problem. This is a Calculus-based course, and
assumes a working knowledge of single-variable calculus as well as some acquaintance with multi-variable calculus
(including multiple integration).
IMPORTANT:
1. The best way to learn this material is to do the homework problems every week.
Please ask me questions about things you don’t understand, either in class or at my office. DON’T wait until you feel
completely lost!
2. It is your responsibility to be aware of any changes the instructor may make to the syllabus as they are announced in
class, or as posted on the course webpage. Students are responsible for all information given when they are absent.
3. The grade I (Incomplete) will be given only if you have a good attendance record, have missed the Final for a good
reason, and otherwise are doing passing work. Makeup exams are not given unless you have missed the exam for a valid
reason and can prove it. Both makeups and incomplete are given at the discretion of the instructor.
4. Cheating will not be tolerated. All incidents of cheating will be reported to the Office of Judicial Affairs. The
University’s cheating policy and related disciplinary actions are detailed in the Student Handbook. The Handbook also
includes a description of what is considered cheating by the University. Cheating in this class includes (but is not limited
to): looking at the papers of others during a quiz or test, talking to other students during a quiz or test.
5. If you have issues with this course and/or instructor which you are not comfortable discussing with your
instructor, you should contact the course coordinator, Hanai Sadaka, at [email protected]. For any matters that
remain unresolved, contact the Teaching Director, Prof. Massey, at [email protected].
6. As a matter of Math Department policy, the I grade (incomplete) will be given only rarely. It is intended to
cover real emergency situations in which a student who is doing reasonably well (C- or better) is unable, due to
circumstances beyond the student's control, to complete all course requirements (e.g., is unable to take the final
exam due to hospitalization). An I grade may not be used to rescue a failing grade, or to postpone the final.
7. All students without legitimate conflicts will take the final exam at the scheduled date and time. Do not make travel
plans that conflict with the final exam.
8. The last day to drop a course without a W grade is Monday February 1. The last day to drop a course with a W grade is
Thursday April 21. The last day to file a Final Exam Conflict Form is Wednesday February 3.
9. Please complete the TRACE evaluations at the end of the course.
Class Schedule & Homework List
Please note that the schedule is very tentative and may be changed at any point. Students are responsible for coming to class and if absent, students still need to be responsible for all material covered and changes announced in class. It is the students’ responsibility to check emails and Blackboard. Week
Jan. 11-14
Sec.
2.1
2.2
2.3
2.4
Topic
Introduction
Sample Spaces and the Algebra of Sets
The Probability Function
Conditional Probability
Assignment
2.4
2.5
3.2
3.3
31, 34, 39, 40, 42, 46, 52
11, 12, 16, 18, 19, 20, 23, 25
4, 7, 8, 9, 23
1, 4, 5, 7, 13, 14
2, 3, 13, 16, 22, 26
1, 2, 4, 6, 9, 12
1, 2, 7, 12, 16, 21, 24, 25, 26
Jan. 25-28
3.3
3.4
Continued
Independence
Binomial Probabilities
Discrete Random Variables
1/18 Martin Luther King Day: No Classes
Continued
Continuous Random Variables
Feb. 1-4
3.5
3.6
Expected Values
The Variance
1, 8, 12, 18, 20(a), 27
2, 5-8, 11
Feb. 8-11
3.7
3.9
Joint Densities
Further Properties of the Mean and Variance
The Poisson Distribution
The Normal Distribution
Exam Review
2/15 President’s Day, no classes
1, 8, 10, 17, 19, 23, 40, 45
13, 16, 17, 20
Jan. 18-21
Feb. 15-18
4.2
4.3
Feb. 22-25
4.3
Feb. 29-Mar. 3 5.2
5.3
Mar. 7-11
Mar. 14-17
Mar. 17-21
Mar. 21-24
Mar. 28-31
Apr 4-7
Apr.11-14
Apr. 18-21
Abr. 22-29
First 1 hour exam on Feb. 19
Continued
Estimating Parameters
Interval Estimation
Spring Break
5.3
5.4
Continued
Properties of Estimators
6.2
6.3
6.4
7.2
7.3
7.4
7.5
9.2
The Decision Rule –hypothesis tests
Testing Binomial Data
Type I and Type II Errors
The t-distribution
Deriving the t-distribution
Drawing Inferences about
Drawing Inferences about
Testing : Exam Review
Second 1 hour exam on April 7
The F-test
Binomial Data: Testing :
Review
4/18 Patriot Day, no class
Review
4/21 Reading Day, no class
9.3
9.4
Final Exams
Quiz 1
Thursday
Jan. 21
1, 3, 5, 8-10
Quiz 2
Thursday
Feb. 4
10, 17, 20, 21
2, 5, 8, 14, 16, 17, 21, 22
27, 30, 33, 35
Exam 1
Wednesday
Feb. 25
1, 3-7, 10, 11
1, 2, 4, 5, 11, 14, 26
5, 9, 11
1, 3, 4, 6, 7, 9, 10, 11
1-4, 6
1, 4, 5, 7, 8, 9, 10
13
1, 2, 7-9, 12
Quiz 3
Thursday
Mar. 17
Quiz 4
Thursday
Mar. 24
1-10
2-5, 7
1-5
Exam 2
Monday
Apr. 7