Statistical and Stochastic Concepts Course Description and Course Learning Objectives

Course Description:

The goal of this course is to teach students statistical and stochastic concepts, methods and models through examples, help students relate stochastic models to real life problems, and also encourage students to develop critical thinking skills that will allow them to realize greater success as mathematics major

This course introduces probabilistic methods for analyzing random processes that allows students to develop probabilistic intuition, learn to pose problems, and ask relevant questions.

Student should have an operational familiarity with the following basic probability concepts: sample space, events, probability axioms, basic rules of probability, independence, equally likely outcomes and counting arguments, conditional probability, Bayes’ Theorem, random variable, probability density function (pdf), probability mass function (pmf), cumulative distribution function (cdf), expected value, moments, moment generating function, variance, standard deviation, covariance, correlation, conditional distribution. The operational familiarity will enable the student to pose solution techniques resulting from mathematical inquiry of identified stochastic processes.

After completing the course, the student should be able to accomplish these Course Learning Objectives (CO):

1. Use Basic Probability Concepts in modeling of Stochastic Processes.

2. Use Stochastic Processes to model real world activities.

3. Apply the Exponential Distribution and Poisson Process to Stochastic Models.

4. Apply Discrete-Time Markov Chains to real world situations.

5. Apply Continuous-Time Markov Chains to real world situations.

6. Use Stochastic Processes to construct Birth and Death Processes Models.

7. Model Queuing Systems using Stochastic Processes. 

LO1.1 Discuss basic probability associated with stochastic processes (CO1).

LO1.2 Apply statistical definitions and key terms to research involving stochastic processes (CO1, CO2).Assignment(s)

1. Prepare for the Final Examination. Students should allot 3 hours of uninterrupted internet time to complete the final exam. Additionally, Students should review any special instructions issued by the instructor.

2. Complete Discussion Question 4 no later than Wednesday of Week 8 and reply to at least two classmates’ postings by Sunday of Week 8. (45 points)

3. Take the 3 hour Final Examination. All exams must be taken prior to the last day of the class. No exams will be administered or accepted after the last day of class unless a student has a valid approved extension.

(Students are reminded that if an extension is required, it must be submitted and approved by the last day of class. Please allow a minimum of two days prior to the last day of class to submit for an extension. Students should not attempt to submit for an extension within the last two days of class end. It may not be approved and returned to the student requesting additional information or specific and detailed dates regarding completion of outstanding course requirements. No extensions will be granted once the semester has ended).

4. Complete Final Examination by 11:59PM Eastern time on the last day of the semester. (200 points)

Course grading will be based on Discussions participation (includes discussion questions, weekly summaries, and other data analysis activities), five graded data projects, and a final examination.

Discussion Questions: There will be discussion questions established for Weeks 1, 3, 5, and 7. Students responses are due 11:59 pm, Wednesdays of Weeks 2, 4, 6, and 8. Responses to a minimum of two classmates postings are due 11:59 pm, Sundays of Weeks 2, 4, 6, and 8. Maximum assessment for each week is 50 points of the 1000 points for the course (40 points for response and

Course Scope

10 points for comments to classmates). Each student is required to participate in the discussion question discussion; initial responses will not be accepted or be given credit after the due date.

Participation (submission of response) outside of any particular week will not be given credit. There are no exceptions to this policy. Additionally, students will not be able to pre-post discussion questions.

Interim Summary Reports: The interim summary reports are the second component of class participation. This report must be completed by the end of Weeks 3, 5, and 7 of the course (Sunday, 11:59 PM Eastern Time or 2350 hours). Late assignments will not be accepted. There are no exceptions to this policy. Maximum assessment for each weekly summary report is 30 points of the 1000 points available in the course. For the interim summary report, each student is required to complete a summary report to include the following as a minimum: What was learned over the previous weeks since last interim summary; identification and presentation of a practical research application (not a problem) from the course materials covered during the period; and a summary of the student’s thoughts on the material covered during the period.

In addition, student should share links to any web sites used to help support learning and understanding of the materials for that week (outside of the tutorials). Student’s interim reports will be evaluated for clarity, quality, content, and proper use of terms, spelling, and grammar. Students will post their summaries in the discussion for Interim Summary Reports for weeks 3, 5, and 7. Interim Summary Reports posted in discussions other than the Interim Summary Reports Discussion will not be accepted or graded; there are no exceptions to this policy. Summaries must be posted as a separate thread. If not posted as a separate thread, it will not be accepted or graded.

Each student is encouraged to comment on other students summaries. Additionally, students are not to use the summary to ask questions; questions should be posted in the “Q &A” Discussion.

Other instructor directed activities: If required, the instructor will post additional activities and they will be noted in the Weekly Announcement. The weekly discussion is a tool for the students to use to communicate their questions and comments. Please make full use of the discussion by asking questions or making comments on the materials covered during any particular week. Do not ask for assistance on particular quiz or exam questions unless it is for clarification.

Quizzes: The four graded Quizzes are dispersed throughout the course (see course schedule). They are worth 125 points each. These quizzes are posted under Quizzes in the Classroom. Student must submit their completed Quiz by the established due date.

Final Exam: The Final Exam will be taken during the last week of the semester. The Final Exam will be worth 200 points toward student’s final course grade. The final exam will cover all materials in the course. Students will have 3 hours to complete the 20 question exam. (Students should make sure that adequate time is allocated to take the exam). The final exam will not be a proctored exam. Students may use the textbook and notes in completing the final exam, but no help from anyone. The Final Exam is posted under Quizzes in the Classroom.

Students’ final grades will be posted as soon as the instructor receives and evaluates the Final Exam. Official grades will continue to be issued by the University on the grade report form. Professors have 7 days from the end of the semester to submit their grades to the University.

The points earned on the graded course assignments will determine the course grade. The final grade in the course will be based on total points.