Math 244: Introduction to Probability Theory
Fall 2017 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: opics include basic probability theory in discrete and continuous sample space, conditional probability and independence, Bayes' theorem and event trees, random variables and their distributions, joint distribution and notion of dependence, expected values and variance, moment generating functions, useful parametric families of distributions including binomial, geometric, hypergeometric, negative binomial, exponential, gamma, normal and their applications, simple case of central limit theorem and its uses.
Number of Credits: 3
Prerequisites: MATH 112 with a grade of C or better or MATH 133 with a grade of C or better.
Course-Section and Instructors
| Course-Section |
Instructor |
| Math 244-001 |
Professor S. Dhar |
Office Hours for All Math Instructors: Fall 2017 Office Hours and Emails
Required Textbook:
| Title |
Probability and Statistics for Engineers and Scientists |
| Author |
Walpole, et al. |
| Edition |
9th |
| Publisher |
Prentice Hall |
| ISBN # |
0-321629116 |
University-wide Withdrawal Date: The last day to withdraw with a W is Monday, November 6, 2017. It will be strictly enforced.
Course Goals
Course Objectives: Train students in the calculus of probability. Topics include basic probability theory in discrete and continuous sample space, conditional probability and independence, Bayes' theorem, random variables and their distributions, joint distribution and notion of dependence, expected values and variance, moment generating functions, parametric families of distributions including binomial, multinomial geometric, hypergeometric, exponential, gamma, normal.
Course Outcomes: On successful completion student will be able to demonstrate understanding of:
- Discrete and continuous random variables and their cumulative distribution function.
- Random vectors, their joint distributions, and marginal and conditional distributions.
- The Bayes theorem, independence, expectation, and moment generating functions.
- Distributions such as binomial, multinomial, geometric, Poisson, normal, and gamma.
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% |
| Class Participation |
10% |
| Midterm Exam |
35% |
| Final Exam |
35% |
Your final letter grade will be based on the following tentative curve. It ensures at least few A’s. Practice problems, HW and Quiz assignments are posted on Math 244 Course Moodle page. Homework is generally due within a week unless announced otherwise by the instructor. Solutions to the assignments will be handed out in class and discussed (see the Math 244 Course Moodle page). Late homework cannot be accepted, since the solutions are already handed out.
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. Absence will affect the grade due to class participation requirement (10% of the grade).
Homework Policy: No late homework will be accepted.
Exams: There will be one midterm exam held in class during the semester and one comprehensive final exam. Exams are held on the following days:
| Midterm Exam I |
November 2, 2017 |
| Final Exam Period |
December 15 - 21, 2017 |
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.
Course Policies: It is required that the student read the textbook for the material already covered in class by the instructor and confirm that the basic solved problems are understood and practice solving textbook problems. More explicitly, students must work on the examples and exercises and problems from the textbook on the topics already covered in class, and learn to solve them correctly. The student should compare his or her answers with those given at the end of the textbook or by the instructor. Instructor holds the right to modify in class exams, homework, quizzes dates in the best interest of the class. Official announcements are made using NJIT student emails or emails provided by students to NJIT as official emails.
- Any complaints regarding grading have to be presented immediately after receiving the graded quizzes / tests.
- Looking into your neighbors work during exams is not allowed. Keeping eyes hidden using hats, caps, etc. during exams is not allowed.
- Instructors will maintain a detailed record of you attendance which is reported to the NJIT administration.
- The use of laptops, cell phones, beepers, or any sort of communication devices (text messaging, internet, notepad, etc.) during regular classes, exams and quizzes are not allowed. Please note that the laptop should remain shut down during lecture time in class.
- 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.
Cellular Phones: All cellular phones and other electronic devices must be switched off during all class times.
Additional Resources
Math Tutoring Center: Located in the Central King Building, Lower Level, Rm. G11 (See: Fall 2017 Hours)
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: Disability Support Services (DSS) offers long term and temporary accommodations for undergraduate, graduate and visiting students at NJIT.
If you are in need of accommodations due to a disability please contact Chantonette Lyles, Associate Director of Disability Support Services at 973-596-5417 or via email at lyles@njit.edu. The office is located in Fenster Hall Room 260. A Letter of Accommodation Eligibility from the Disability Support Services office authorizing your accommodations will be required.
For further information regarding self identification, the submission of medical documentation and additional support services provided please visit the Disability Support Services (DSS) website at:
Important Dates (See: Fall 2017 Academic Calendar, Registrar)
| Date |
Day |
Event |
| September 5, 2017 |
T |
First Day of Classes |
| September 11, 2017 |
M |
Last Day to Add/Drop Classes |
| November 6, 2017 |
M |
Last Day to Withdraw |
| November 21, 2017 |
T |
Thursday Classes Meet |
| November 22, 2017 |
W |
Friday Classes Meet |
| November 23 - 26, 2017 |
R - Su |
Thanksgiving Break - University Closed |
| December 13, 2017 |
W |
Last Day of Classes |
| December 14, 2017 |
R |
Reading Day |
| December 15 - 21, 2017 |
F - R |
Final Exam Period |
Course Outline
| Week |
Date |
Section |
Topic |
| 1 |
9/7 |
2.1-2.3 |
Sample space, events, counting |
| 2 |
9/11 |
2.1-2.3 |
Counting- continued |
| 2 |
9/14 |
2.4 |
Probability of an event |
| 3 |
9/18 |
2.5 |
Additive rules |
| 3 |
9/21 |
2.6 |
Conditional probability, independence |
| 4 |
9/25 |
2.6 |
Product rules |
| 4 |
9/28 |
2.7-2.8 |
Bayes' rule |
| 5 |
10/2 |
3.1 |
Concept of a random variable |
| 5 |
10/5 |
3.2 |
Discrete probability distributions |
| 6 |
10/9 |
3.3 |
Continuous probability distributions |
| 6 |
10/12 |
3.3 |
Continuous probability distributions - continued |
| 7 |
10/16 |
3.4-3.5 |
Joint probability distributions |
| 7 |
10/19 |
3.4-3.5 |
Joint probability distributions - continued |
| 8 |
10/23 |
4.1-4.2 |
Mean and covariance of random variables (RV) |
| 8 |
10/26 |
4.3 |
Mean and Variance of Linear RV’s |
| 9 |
10/30 |
|
REVIEW |
| 9 |
11/2 |
|
MIDTERM EXAM (NOV 13) |
| 10 |
11/6 |
5.1-5.2 |
Binomial distribution |
| 10 |
11/9 |
5.3 |
Hypergeometric distribution |
| 11 |
11/13 |
5.4 |
Negative Binomial distribution |
| 11 |
11/16 |
5.5-5.6 |
Poisson distribution |
| 12 |
11/20 |
5.5-5.6 |
Poisson distribution- continued |
| 12 |
11/21 |
6.1-6.3 |
Continuous uniform and Normal distributions |
| 13 |
11/27 |
6.4-6.5 |
Normal approximation to the Binomial |
| 13 |
11/30 |
6.6 |
Gamma and Exponential distributions |
| 14 |
12/4 |
7.1-7.3 |
Transformations and moment generating functions |
| 14 |
12/7 |
7.1-7.3 |
Transformations and moment generating functions - continued |
| 15 |
12/11 |
|
REVIEW |
Grade Criteria for Class Participation (out of a maximum of 4)
Once the student names are uniquely identified, from there onwards each student will receive a score of 0 to 4 at the end of the each class according to the following criteria:
0: Student is absent (please give proof of extenuating circumstance). Student has sustained attention on laptop/electronic devices. Not participating in the class at all. She/he is disruptive and says little or nothing in class. Contributions in class reflect inadequate preparation. Ideas offered are seldom substantive, provides few if any insights, and never a constructive direction for the class. Integrative comments are absent. If this person were not a member of the class, valuable class-time would be saved.
1: Student is present and not disruptive. Tries to respond when called on but does not offer much. Student demonstrates very infrequent involvement in class discussion. This person says little or nothing in class. Hence, there is not an adequate basis for evaluation. If this person were not a member of the class, the quality of discussion would not be changed.
2: Student demonstrates adequate preparation: knows basic facts, but does not show evidence of trying to interpret or analyze them. She/he offers straightforward information (e.g., straight from the textbook), without elaboration or very infrequently (perhaps once a class). Does not offer to contribute to discussion, but contributes to a moderate degree when called on. Student demonstrates sporadic involvement. Contributions in class reflect satisfactory preparation. Ideas offered are sometimes substantive, provides generally useful insights but seldom offer a new direction for the discussion. If this person were not a member of the class, the quality of discussion would be diminished somewhat.
3: Student demonstrates good preparation: knows covered course material well, has thought through implications of them. She/he offers interpretations and analysis of course material (more than just facts) to class. Student contributes well to discussion in an ongoing way: responds to other students' points, thinks through their own points, questions others in a constructive way, offers and supports suggestions that may be counter to the majority opinion. Student demonstrates consistent ongoing involvement. Contributions in class reflect thorough preparation. Ideas offered by the student are usually substantive; provide good insights, and sometimes direction for the class. If this person were not a member of the class, the quality of discussion would be diminished.
4: Student demonstrates excellent preparation: has analyzed covered course material exceptionally well, relating it to readings and other material (e.g., readings, course material, etc.). She/he offers analysis, synthesis, and evaluation of covered course material, e.g., puts together pieces of the discussion to develop new approaches that take the class further. Student contributes in a very significant way to ongoing discussion: keeps analysis focused, responds very thoughtfully to other students' comments, contributes to the cooperative argument-building, suggests alternative ways of approaching material and helps class analyze which approaches are appropriate, etc. She/he demonstrates ongoing very active involvement. Contributions in class reflect exceptional preparation. Ideas offered are always substantive, and provide one or more major insights as well as direction for the class. If this person were not a member of the class, the quality of discussion would be diminished markedly.
The average score out of the maximum of 4 is used to calculate the class participation score.
Updated by Professor S. Dhar - 9/1/2017
Department of Mathematical Sciences Course Syllabus, Fall 2017
