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MATH 662 Course Syllabus
NJIT HONOR CODE: All Students should be aware that the Department of Mathematical Sciences takes the NJIT Honor Code 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 Honor Code, students are obligated to report any such activities to the Instructor.
Math 662-101: Probability Distributions
FALL 2009
Textbook: Introduction to Mathematical Statistics (Sixth Edition), by Robert V. Hogg, Joseph W. McKean and Allen T. Craig. ISBN: 0-13-008507-3.
Prerequisites: This course is part of the Math 662 - Math 762 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.
Grading Policy: The final grade in this course will be determined as follows:
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▪ Homework & Quizzes: |
20% |
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▪ Midterm Exams: |
50% |
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▪ Final Exam: |
30% |
Drop Date: Please note that the University Drop Date November 2, 2009 deadline will be strictly enforced.
References:
▪ Introduction to the Theory of Statistics, by Mood, Graybill and Boes, Third Edition.
▪ Probability and Statistics, by Morris H. DeGroot and Mark J. Schervish, Third Edition.
▪ A Course in Mathematical Statistics, George G. Roussas, Second Edition. (Has certain solutions to both odd and even problems).
Homework & Quizzes: There will be 13 homework plus quizzes that will account for 20% of the final grade in this course.
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: |
October 5, 2009 |
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Exam 2: |
November 16, 2009 |
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Final Exam: |
December 14, 2009 |
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:
▪ Any complaints regarding grading have to be presented immediately after receiving the graded tests.
▪ Please, always bring a statistics calculator (without graphing capabilities) to your quizzes, exams and to all the lectures.
▪ Looking into your neighbors work during exams is not allowed. Keeping eyes hidden using hats, caps, etc. during exams is not allowed.
▪ 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 Holiday ~ University Closed |
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| M |
Last Day to Withdraw from this course |
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| T |
Classes follow a Thursday Schedule |
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November 25, 2009 |
W |
Classes follow a Friday Schedule |
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November 26-29, 2009 |
R-Su |
Thanksgiving Recess ~ University Closed |
Course Outline:
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Week |
Chapter & Topic |
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Week
1 |
Chapter 1.3-1.5 |
Probability & Distributions |
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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.). |
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Week
2 |
└► |
(Mon. Sept. 7) Labor Day Holiday ~ University Closed |
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Week
3 |
Chapter 1.6-1.8 |
Probability & Distributions |
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Transformations, expected value of a random variable, some special expectations. |
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Week
4 |
Chapter 1.9-1.10 |
Probability & Distributions |
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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. |
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Week
5 |
Chapter 2.1-2.3 |
Multivariate Distributions |
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Distribution of two random variables, transformations, conditional distributions and expectations. |
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Week
6 |
└► |
MIDTERM EXAM I: Monday ~ October 5, 2009 |
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Week
7 |
Chapter 2.4-2.6 |
Multivariate Distributions |
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Correlation coefficient, independent random variables, extension to several random variables. |
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Week
8 |
Chapter 2.7, 3.1-3.2 |
Multivariate Distributions, Some Special Distributions |
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Random vector transformation, binomial and related distributions: geometric, negative binomial. Hypergeometric distribution, Poisson distribution. |
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Week 9 |
Chapter 3.3-3.5 |
Some Special Distributions |
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Exponential, gamma, uniform distribution chi-squared, beta and normal distributions. Multivariate Normal distribution. |
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Week
10 |
└► |
(Mon. Nov. 2) Last Day to Withdraw from this course |
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Chapter 3.6-3.7, 4.1 |
Some Special Distributions, Unbiasedness |
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t and F-distributions, distribution of sample mean and variance under normality, mixture distributions. Expectation of functions. |
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Week
11 |
Chapter 4.2-4.3 |
Convergence in Probability, Convergence in Distribution |
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Week 12 |
└► |
MIDTERM EXAM II: Monday ~ November 16, 2009 |
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Week 13 |
Chapter 4.3 |
Delta Method, MGF Technique |
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Week 14 |
Chapter 4.4 |
Central Limit Theorem |
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Week 15 |
Chapter 5.1-5.2 |
Sampling and Statistics, Order Statistics |
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Final |
Final EXAM: Monday ~ December 14, 2009 |
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Prepared By: Prof. Sunil Dhar
Last revised: August 3, 2009