# Math 333: Probability and StatisticsSpring 2018 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: Descriptive statistics and statistical inference. Topics include discrete and continuous distributions of random variables, statistical inference for the mean and variance of populations, and graphical analysis of data.

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 333-004 Professor P. Natarajan
Math 333-008 Professor D. Schmidt
Math 333-010 Professor D. Schmidt
Math 333-014 Professor P. Natarajan
Math 333-018 Professor M. Michal
Math 333-028 Professor S. Mahmood
Math 333-102 Professor J. Porus

Office Hours for All Math Instructors: Spring 2018 Office Hours and Emails

Required Textbook:

 Title Applied Statistics and Probability for Engineers Author Montgomery and Runger Edition 6th Publisher John Wiley & Sons ISBN # 978-1118963548 (Custom Ed. Bundled w/ WP) 978-1118470688 (Standalone WP Registration Card)

University-wide Withdrawal Date:The last day to withdraw with a w is Monday, April 2, 2018. It will be strictly enforced.

## Course Goals

Course Objective: The objective of this course is to acquaint students with probability, descriptive statistics and statistical inference and demonstrate real world applications using examples drawn from various fields.

### Course Outcomes

• Demonstrate understanding of various statistical terms and methods for summarizing, organizing, and presenting data.
• Compute measures of central tendency, position, and variability and interpret them.
• Describe sample space and events and demonstrate their knowledge of various counting techniques, notions of probability, random variables and various discrete and continuous probability distributions.
• Demonstrate conceptual understanding of sampling distributions and the central limit theorem.
• Perform statistical analysis, such as estimation, hypothesis testing, regression, and draw conclusions.

Course Assessment: The assessment tools used will include quizzes and weekly homework assignments, two common mid-term exams, and a common 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 15% Common Midterm Exam I 25% Common Midterm Exam II 25% Final Exam 35%

Your final letter grade will be based on the following tentative curve.

 A 90 - 100 C 65 - 74 B+ 85 - 89 D 55 - 64 B 80 - 84 F 0 - 54 C+ 75 - 79

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/ Quiz Policy: Online Weekly Homework will be assigned on WileyPlus. Additional Homework and/or Quizzes would be given in class.

Exams: There will be two common midterm exams held during the semester and one comprehensive common final exam. Exams are held on the following days:

 Common Midterm Exam I February 28, 2018 Common Midterm Exam II April 11, 2018 Final Exam Period May 4 - 10, 2018

The time of the midterm exams is 4:15-5:40 pm for daytime students and 5:45-7:10 pm for evening students. 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.

Calculator Policy: Only a basic (non-programmable and non-graphing) calculator is permitted during the exams.

Makeup Exam Policy: To properly report your absence from a midterm or final exam, please review and follow the required steps under the DMS Examination Policy found here:

Cellular Phones: All cellular phones and other electronic devices must be switched off during all class times.

Math Tutoring Center: Located in the Central King Building, Lower Level, Rm. G11 (See: Spring 2018 Hours)

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: Spring 2018 Academic Calendar, Registrar)

Date Day Event
January 16, 2018 T First Day of Classes
January 22, 2018 M Last Day to Add/Drop Classes
March 11 - 18, 2018 Su - Su Spring Recess - No Classes/ University Closed
March 30, 2018 F Good Friday - No Classes/ University Closed
April 2, 2018 M Last Day to Withdraw
May 1, 2018 T Friday Classes Meet - Last Day of Classes
May 2 - 3, 2018 W - R Reading Days
May 4 - 10, 2018 F - R Final Exam Period

# Course Outline

Week Class Lec. Section Topic Exercise Problems for Additional HW/ Practice
Week  1
1/16 (T)
1 1 6.1 Descriptive statistics: Numerical Summaries of data: Sample Mean, Sample Variance, Sample Standard Deviation, Range 6.8, 6.9, 6.12, 6.14
2 2 6.2 Descriptive statistics: Stem and Leaf Diagram, Mean, Median, Quartiles, Interquartile Range 6.30, 6.32, 6.36, 6.38, 6.44
Week 2
1/23 (T)
3 3 6.3, 6.4 Descriptive statistics: Histograms, Boxplot 6.46, 6.54, 6.69, 6.74, 6.79, 6.80
4 4 2.1, 2.2, 2.3 Probability: Sample Spaces and Events; Interpretations and Axioms of Probability; Addition rules 2.35, 2.41, 2.42, 2.45, 2.47 ab, 2.58, 2.60, 2.67, 2.70, 2.71, 2.76, 2.84, 2.86, 2.88
Week 3
1/30 (T)
5 5 2.4, 2.5, 2.6 Probability: Conditional Probability; Multiplication and Total Probability Rules; Independence 2.99, 2.100, 2.102, 2.105, 2.106, 2.107, 2.108, 2.124, 2.126, 2.128, 2.145, 2.146, 2.148, 2.149, 2.156, 2.157, 2.187, 2.208, 2.224
6 6 2.7 Probability: Bayes' theorem 2.166, 2.170, 2.172, 2.173, 2.185, 2.220
Week 4
2/6 (T)
7 7 3.1, 3.2, 3.3 Discrete Random Variables and Probability Distributions: Discrete Random Variables; Probability Distributions and Probability Mass Functions; Cumulative Distribution Functions 3.18, 3.24, 3.25, 3.30, 3.39, 3.40, 3.45, 3.50, 3.51, 3.197, 3.201
8 8 3.4, 3.5 Discrete Random Variables and Probability Distributions: Mean and Variance of a Discrete Random Variable;  Discrete Uniform Distribution 3.60, 3.62, 3.64, 3.78, 3.81, 3.83, 3.175
Week 5
2/13 (T)
9 9 3.6 Discrete Random Variables and Probability Distributions: Binomial Distribution; 3.95, 3.100, 3.101, 3.102, 3.103, 3.104, 3.106, 3.119, 3.120, 3.123, 3.198
3.7 Geometric Distribution only from Section 3.7
10 10 3.9 Discrete Random Variables and Probability Distributions: Poisson Distribution   3.160, 3.163, 3.164, 3.167, 3.168, 3.190, 3.192
Week 6
2/20 (T)
11 11 4.1, 4.2, 4.3 Continuous Random Variables and Probability Distributions: Continuous Random Variables; Probability distributions and Probability Density Functions; Cumulative Distribution Functions    4.1, 4.4, 4.5, 4.6, 4.8, 4.9, 4.17, 4.18, 4.19, 4.29
12 12 4.4, 4.5 Continuous Random Variables and Probability Distributions: Mean and Variance of a Continuous Random Variable; Continuous Uniform Distribution 4.35, 4.36, 4.38, 4.39, 4.52, 4.53, 4.54, 4.56
Week 7
2/27 (T)
13 REVIEW FOR EXAM #1
MIDTERM EXAM I:
Wednesday ~ February 28, 2018
14 13 4.8 Continuous Random Variables and Probability Distributions: Exponential Distribution 4.116ab, 4.117, 4.119, 4.121, 4.125, 4.126, 4.132
Week 8
3/6 (T)
15 14 4.6 Continuous Random Variables and Probability Distributions: Normal distribution 4.63, 4.66, 4.71, 4.72, 4.76, 4.78
16 15 4.7 Continuous Random Variables and Probability Distributions: Normal Approximation to the Binomial and Poisson Distributions 4.98, 4.99, .4.103
3/11(S) to 3/18(S)  - SPRING RECESS  (NO CLASSES)
Week 9
3/20 (T)
17 16 7.1- 7.2 Point estimation of Parameters and Sampling Distributions: Point Estimation; Sampling Distributions and the Central Limit Theorem 7.5, 7.7, 7.8, 7.11, 7.12
18 17 8.1 Statistical Intervals for a Single Sample: Confidence interval on the Mean of a Normal distribution, Variance Known 8.10, 8.11, 8.12, 8.13, 8.21
Week 10
3/27 (T)
19 18 8.2 Statistical Intervals for a Single Sample: Confidence Interval on the Mean of a Normal Distribution, Variance Unknown 8.25, 8.30, 8.31, 8.38bc, 8.39 bc
20 19 8.3 Statistical Intervals for a Single Sample: Confidence intervals on the Variance and Standard deviation of a Normal Distribution 8.47, 8.48, 8.49, 8.50, 8.51
(WITHDRAWAL DEADLINE:  Monday, April 2, 2018
Week 11
4/3 (T)
21 20 8.4 Statistical Intervals for a Single Sample: Large-Sample Confidence Interval for a Population Proportion 8.60, 8.61, 8.62, 8.63, 8.64
22 21 9.1- 9.2 Tests of Hypotheses for a Single Sample: Hypothesis Testing; Tests on the Mean of a Normal Distribution, Variance Known 9.31, 9.32, 9.35, 9.36, 9.37
Week 12
4/10 (T)
23 REVIEW FOR EXAM #2
MIDTERM EXAM II:
Wednesday ~ April 11, 2018
24 22 9.1- 9.2 Tests of Hypotheses for a Single Sample: Tests on the Mean of a Normal Distribution, Variance Known 9.15, 9.43, 9.47, 9.48, 9.49
Week 13
4/17 (T)
25 23 9.3.1 Tests of Hypotheses for a Single Sample: Tests on the Mean of a Normal Distribution, Variance Unknown 9.52, 9.53, 9.55, 9.56, 9.63a, 9.64a
26 24 9.5 Tests of Hypotheses for a Single Sample: Tests on a Population Proportion 9.92, 9.93, 9.94, 9.95
Week 14
4/24 (T)
27 25 10.4 Statistical Inference for Two Samples: Paired t-test 10.53, 10.54, 10.55
10.1 Inference on the Difference in Means of Two Normal Distributions, Variances known 10.1ab, 10.2ab, 10.3 ab, 10.6ab, 10.7ab
28 26 11.2 Simple Linear Regression and Correlation: Simple Linear Regression 11.1ab, 11.2 ab, 11.8ab
REVIEW FOR FINAL EXAM
Week 15
5/1 (T)
May 1(Tuesday): Friday classes meet
REVIEW FOR FINAL EXAM
Reading Day 5/2 and 5/3 (W & R)
5/4 - 5/10 Final EXAM WEEK

Updated by Professor P. Natarajan - 1/10/2018
Department of Mathematical Sciences Course Syllabus, Spring 2018