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MATH 662 Course Syllabus
- fall 2012
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.
Math 662: Probability Distributions
Number of Credits: 3
Course Description: Probability, conditional probability, random variables and distributions, independence, expectation, moment generating functions, useful parametric families of distributions, transformation of random variables, order statistics, sampling distributions under normality, the central limit theorem, convergence concepts and illustrative applications.
Prerequisites: This course is part of the Math 662 - Math 665 sequence. Prerequisite must be satisfied. In case of doubt, contact the instructor to find out if you have satisfied the required prerequisite: Math 341 or Math 333 and departmental approval.
Textbook: Introduction to Mathematical Statistics (Seventh Edition), by Robert V. Hogg, Joseph W. McKean and Allen T. Craig.
Instructor: (for specific course-related information, follow the link below)
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Math 662-101 |
Grading Policy: The final grade in this course will be determined as follows:
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▪ Hand-in Hw & Quizzes: |
20% |
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▪ Midterm Exams I and II: |
50% |
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▪ Final Exam: |
30% |
Drop Date: Please note that the University Drop Date November 6, 2012 deadline will be strictly enforced.
References:
▪ Introduction to the Theory of Statistics, by Mood, Graybill and Boes, Third Edition.
▪ A Course in Mathematical Statistics, George G. Roussas, Second Edition. (Has certain solutions to both odd and even problems).
▪ For PhD students in Statistics: Statistical Inference (chapters 1-5), by Casella and Berger, Second edition (Duxbury Advanced Series).
Homework Policy: No late homework will be accepted.
Attendance & Participation: Students must attend all classes. Absences from class will inhibit your ability to fully participate in class discussions and problem solving sessions and, therefore, affect your grade. Tardiness to class is very disruptive to the instructor and students and will not be tolerated.
Examinations: Two in-class midterm examinations and one final examination will be given on the following days.
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Exam 1: |
, 2012 |
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Exam 2: |
, 2012 |
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Final Exam Week: |
December 14-20, 2012 |
Your final letter grade will be based on the following tentative curve. This curve may be adjusted slightly at the end of the semester.
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A |
90-100 |
C |
40-54 |
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B+ |
75-89 |
F |
0-39 |
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B |
65-74 |
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C+ |
55-64 |
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Makeup Exam Policy: There will be No make-up EXAMS during the semester. In the event the Final Exam is not taken, under rare circumstances where the student has a legitimate reason for missing the final exam, a makeup exam will be administered by the math department. In any case the student must notify the Math Department Office and the Instructor that the exam will be missed and present written verifiable proof of the reason for missing the exam, e.g., a doctors note, police report, court notice, etc., clearly stating the date AND time of the mitigating problem.
Additional Policies:
▪ Please, always bring a statistics calculator (without graphing capabilities) to your quizzes, exams and to all the lectures.
▪ Attendance at all classes and tests is required. Instructors will maintain a detailed record of you attendance as the administrators need to know the dates you missed classes.
▪ The use of laptops, cell phones, beepers, or any sort of communication devices (internet use, palm pilot, etc) during regular classes, exams and quizzes are not allowed.
▪ No eating allowed during the class and exams periods. You are expected to remain in the classroom for the entire class period. Wandering in and out of the classroom is not allowed.
Further Assistance: For further questions, students should contact their Instructor. All Instructors have regular office hours during the week. These office hours are listed at the link above by clicking on the Instructor’s name. Teaching Assistants are also available in the math learning center.
Cellular Phones: All cellular phones and beepers must be switched off during all class times.
MATH DEPARTMENT CLASS POLICIES LINK
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. For DMS Course Policies, please click here.
| M |
Labor Day ~ No classes |
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| T |
Last Day to Withdraw from this course |
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| T |
Classes follow a Thursday Schedule |
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| W |
Classes follow a Friday Schedule |
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| R-Su |
Thanksgiving Recess |
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| R |
Reading Day |
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| F- R |
Final Exams |
Course Outline:
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Course
Outline |
||||
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Week |
Lecture |
Sections* |
Topic |
Assignment |
|
1 |
1 |
1.3-1.5 |
Probability & Distribution-I:
The
probability set function, conditional probability
and independence, random variables, discrete and
continuous random variables, probability mass
functions (p.m.f.) and density functions (p.d.f.).
|
All Homeworks
will be assigned in class |
|
2 |
2 |
1.6-1.8 |
Probability &
Distributions-II:
Transformations, expected value of a random
variable, some special expectations |
|
|
3 |
3 |
1.9-1.10 |
Probability &
Distributions:-III:
Moment generating functions (m.g.f.), important
inequalities. Functions of a single r.v., the
generalized inverse of a c.d.f., a transformation of
any r.v. leading to uniform distribution,
relationship to simulation |
|
|
4 |
4 |
2.1-2.3 |
Multivariate Distributions-
I:
Distribution of two random variables, transformations,
conditional distributions and expectations. |
|
|
5 |
5 |
2.4-2.5 |
Multivariate Distributions-
II:
Correlation coefficient, independent random variables, extension
to several random variables. |
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|
6 |
6 |
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MIDTERM EXAM –I |
|
|
7 |
7 |
2.7, 3.1-3.2 |
Some Parametric Families of Distributions-I:
binomial and related distributions: geometric,
negative binomial. Hypergeometric distribution,
Poisson distribution; Exponential, uniform
distributions |
|
|
8 |
8 |
3.3-3.4 |
Some Parametric Families of Distributions-II:
Gamma, Chi-squared,
beta and normal
distributions. Multinomial distributions |
|
|
9 |
9 |
3.5-3.6 |
Some Parametric Families of Distributions-III:
Multivariate Normal distribution, t and F distributions |
|
|
10 |
10 |
Chapters 2-3 |
Computing
distributions of Functions of
Random Varibles –I: using method of
transformations |
|
|
11 |
11 |
Chapters 2-3 |
Computing
distributions of Functions of
Random Varibles –II: using other methods
such as m.g.f.s |
|
|
12 |
12 |
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MIDTERM EXAM –II |
|
|
13 |
13 |
4.3-4.4 |
Asymptotic distributions; some basic concepts and
tools:
Convergence in Distribution, Convergence in
probability. Central Limit Theorem, Delta Method |
|
|
14 |
14 |
5.1-5.2 |
Order Statistics:
joint distributions and functions of order statistics |
|
|
15 |
15 |
|
final EXAM |
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*Note: There may be some changes, including exam dates. Any modifications will be announced in class.
Prepared By: Prof. Ji Meng Loh
Last revised: August 27 , 2012