Download Math 341 Syllabus SP16 - Department of Mathematical Sciences

MATH 341: Statistical Methods I
Spring 2016 Course Syllabus
NJIT Academic Integrity Code: All Students should be aware that the Department of Mathematical Sciences
takes the University Code on Academic Integrity at NJIT very seriously and enforces it strictly. This means that
there must not be any forms of plagiarism, i.e., copying of homework, class projects, or lab assignments, or
any form of cheating in quizzes and exams. Under the University Code on Academic Integrity, students are
obligated to report any such activities to the Instructor.
COURSE INFORMATION
Course Description: Covers applications of classical statistical inference. Topics include transformation of
variables, moment generating technique for distribution of variables, introduction to sampling distributions,
point and interval estimation, maximum likelihood estimators, basic statistical hypotheses and tests of
parametric hypotheses about means of normal populations, chi-square tests of homogeneity, independence,
goodness-of-fit. Effective From: Spring 2009.
Number of Credits: 3
Prerequisites: Math 244 with a grade of C or better or Math 333 with a grade of C or better.
Course-Section and Instructors
Course-Section
Math 341-002
Instructor
Professor S. Subramanian
Required Textbook:
Title
Mathematical Statistics with Applications
Author
Wackerly, Mendenhall, and Scheaffer
Edition
7th
Publisher
Thomson Brooks/Cole
ISBN #
978-0495110811
University-wide Withdrawal Date: Please note that the last day to withdraw with a W is March 28, 2016. It
will be strictly enforced.
COURSE GOALS
Course Objectives: Covers applications of classical statistical inference. Topics include transformation of
variables, moment generating technique for distribution of variables, introduction to sampling distributions,
point and interval estimation, maximum likelihood estimators, basic statistical hypotheses and tests, classical
tests of parametric hypotheses about means of normal populations, chi-square tests of homogeneity,
independence, goodness- of-fit.
Course Outcomes
Develop skills in the methods of mathematical statistics.
Learn different estimation techniques such as method of moments, maximum likelihood.
Develop the skills to compute uniformly minimum variance unbiased estimators.
Learn the likelihood ratio test.
Compute confidence intervals.
Compare treatments using ANOVA.
Use Chi-squared test of homogeneity of populations, independence of categorical variables.
Use Chi-squared test to evaluate the goodness-of-fit of data to a specified distribution.
Course Assessment: Will be based on regular homework, two midterm exams and one final exam.
POLICIES
DMS Course Policies: All DMS students must familiarize themselves with, and adhere to, the Department of
Mathematical Sciences Course Policies, in addition to official university-wide policies. DMS takes these policies
very seriously and enforces them strictly.
Grading Policy: The final grade in this course will be determined as follows:
Homework and Quizzes
20%
Midterm Exam I
25%
Midterm Exam II
25%
Final Exam
30%
Attendance Policy: Attendance at all classes will be recorded and is mandatory. Please make sure you read
and fully understand the Math Department’s Attendance Policy. This policy will be strictly enforced.
Homework and Quiz Policy: Regular homework will be assigned. They need to be submitted on the due date
in class. Late homework will not be accepted.
Exams: There will be two midterm exams held in class during the semester and one comprehensive final
exam. Exams are held on the following days:
Midterm Exam I
February 19, 2016
Midterm Exam II
April 15, 2016
Final Exam Period
May 6 - 12,2016
The final exam will test your knowledge of all the course material taught in the entire course. Make sure you
read and fully understand the Math Department's Examination Policy. This policy will be strictly enforced.
Makeup Exam Policy: There will be NO MAKE-UP QUIZZES OR EXAMS during the semester. In the event an
exam is not taken under rare circumstances where the student has a legitimate reason for missing the exam,
the student should contact the Dean of Students office and present written verifiable proof of the reason for
missing the exam, e.g., a doctor’s note, police report, court notice, etc. clearly stating the date AND time of
the mitigating problem. The student must also notify the Math Department Office/Instructor that the exam
will be missed.
Cellular Phones: Cell phones if used for communicating (e.g. texting, etc.) during lecture in the classroom
will be confiscated and returned to the student only at the end of class. All cellular phones and beepers must
be switched off during all class times.
Laptops: Computers and other communication devices should remain closed during lecture time, exams and
quizzes. Grading: Any complaints regarding grading have to be presented immediately after receiving the
graded test, quiz, HW or exam in-class.
Looking into neighbors work during exams: Keeping eyes hidden using hats, caps, etc., from the proctor, but
not from the neighbors work during exams is not allowed.
Wandering: Going in and out of the classroom often is not allowed.
Calculators: Calculators are allowed but should be basic, without graphing capabilities, algebraic
simplification capabilities, formula storing capabilities and without other such capabilities.
ADDITIONAL RESOURCES
Math Tutoring Center: Located in Cullimore, Room 214 (See: Spring 2016 Hours TBA)
Further Assistance: For further questions, students should contact their instructor. All instructors have
regular office hours during the week. These office hours are listed on the Math Department's webpage for
Instructor Office Hours and Emails.
All students must familiarize themselves with and adhere to the Department of Mathematical Sciences Course
Policies, in addition to official university-wide policies. The Department of Mathematical Sciences takes these
policies very seriously and enforces them strictly.
Accommodation of Disabilities: NJIT is committed to providing students with documented disabilities equal
access to programs and activities. If you have, or believe that you may have, a physical, medical,
psychological, or learning disability that may require accommodations, please contact the Coordinator of
Student Disability Services located in the Center for Counseling and Psychological Services, in Campbell Hall,
Room 205, (973) 596-3414. Further information on disability services related to the self-identification,
documentation and accommodation processes can be found on the webpage at:
http://www.njit.edu/counseling/services/disabilities.php
Important Dates (See: Spring 2016 Academic Calendar, Registrar)
Date
Day
Event
January 19, 2016
T
First Day of Classes
January 25, 2016
M
Last Day to Add/Drop Classes
March 13 - 20, 2016
Su - Su
Spring Recess - No Classes, University Open
March 25, 2016
F
Good Friday - No Classes, University Closed
May 3, 2016
T
Friday Classes Meet/ Last Day of Classes
May 4 & 5, 2016
W&R
Reading Days
May 6 - 12, 2016
F-R
Final Exam Period
Course Outline
Lecture
Sections
Topic
Assignment
1
(1- 19)
2.1
One variable transformation;
Section 2.5: 1-4, 6, 7a, 9, 11b,
Section 5.7: 49a,b
2
(1-22)
2.3
Moments and Moment Generating Functions
Section 2.5: 30, 32, 33, 38a
3
(1-26)
4.1
Joint and Marginal Distributions
Section 4.8: 1, 4a, 5, 11, 48a, 49a
4
(1-29)
4.2
Conditional Probability Distributions and Marginal
Distributions and Independence
Section 4.8: 4, 7, 9, 10, 15, 30b, 49b
5
(2-2)
4.3
Bivariate Transformations
Section 4.8: 18 – 22, 51a
6
(2-5)
4.3
Bivariate Transformations
Section 4.8: 23, 24, 27, 28a, 30b,
46c
7
(2-9)
4.4
Conditional Probability Distributions and Marginal
Distributions
Section 4.8: 30a no Cov., 31, 32a, 34
8
(2-12)
(2-16)
4.5
Covariance and Correlation
Section 4.8: 4 and 5 find Correlations
of X and Y, 30a Cov., 49c, 50 first
part.
EXAM 1: FEBRUARY 19TH
9
(2-19)
10
(2-23)
5.1-5.3
Random Samples, Sampling Distributions related to
the Normal Distribution
Section 5.7: 1, 3, 5, 6, 10, 15, 16,
17c, 18b, 34, 36a, 57a,b.
11
(2-26)
5.4
Order Statistics
Section 5.7: 22, 24, 27a
12
(3-1)
5.5
Central Limit Theorem
Section 5.7: 30, 31 with CLT, 37,
51a,b
13
(3-4)
6.2-6.2.15
Sufficient Statistics
Section 6.5: 1, 2, 3, 5, 6, 7, 8, 17
first two parts
14
(3-8)
7.1, 7.2.1
Method of Moments (MOM);
Section7.4: 6c, 8c, 10a, 11b, 18a
15
(3-11)
7.2.2
Maximum Likelihood Estimation (MLE)
Section7.4: 1, 2a, 3, 6ab, 7, 8b, 10a,
11a, 12a, 13
16
(3-22)
7.3.1-7.3.3
Bias and Mean Square Error of Point Estimators,
Uniformly Minimum Variance Unbiased Estimators
(UMVUE)
Section7.4: 1, 7.2a, 8a, 9, 12bc, 46,
49, 50abc-sufficient
17
(3-25)
8.1, 8.2.1
Hypothesis Testing; LRT
Section 8.4: 1, 3, 12, 14
18
(3-29)
8.3.1
Type II error; Power of Tests
Section 8.4: 13ab, 17c, 18, 37c-size,
38a
19
(4-1)
8.3.2
Neyman-Pearson Lemma
Section 8.4: 15, 19, 20, 22, 23
20
(4-5)
8.3.4
p-values
Section 8.4: 2, 49
21
(4-8)
9.1, 9.2.19.2.2
Interval estimation
Section 9.4: 12, 16, 17 with n =1, 37
first part
22
(4-12)
9.3.1
Size and Coverage Probability
Section 9.4: 13ab, 14ab, 25 pivotal
method only. 33a, 34a
23
EXAM 2: APRIL 15TH
(4-15)
24
(4-19)
11.1,
ANOVA for one-way classification
11.2.,11.2.2,
11.2.6
TBA
25
(4-22)
Class Notes
Categorical Data; Goodness-of-Fit Test
TBA
26
(4-26)
Class Notes
Chi-Squared Test of Independence
TBA
27
(4-29)
Class Notes
Chi-Squared Test of Homogeneity
TBA
28
(5-3)
REVIEW
Updated by Professor S. Subramanian - 12/28/2015
Department of Mathematical Sciences Course Syllabus, Spring 2016