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Introduction to Statistical and Stochastic Concepts

## Course Description

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.

Course Scope:
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.

Objectives
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.
CO 2. Use Stochastic Processes to model real world activities.
CO 3. Apply the Exponential Distribution and Poisson Process to Stochastic Models.
CO 4. Apply Discrete-Time Markov Chains to real world situations.
CO 5. Apply Continuous-Time Markov Chains to real world situations.
CO 6. Use Stochastic Processes to construct Birth and Death Processes Models.
CO 7. Model Queuing Systems using Stochastic Processes.

Outline
Week 1: Basic Probability Theory
Learning Objective(s)
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).

Chapter 1
Assignment(s)
1. Students must introduce themselves to the class using the discussion thread created on the Discussion for Week 1 (10 points).

2. Students must read and study this syllabus. The syllabus is the guide to this course. If a student has a question, the question should be posted on the Week 1 Discussion as a separate thread.

3. Students must familiarize themselves with the classroom. The instructor will post a weekly announcement (first page seen upon entering the classroom). Students must review the Weekly Announcements for key items, guidance, and special assignments. Additionally students should be familiar with the Discussions, Resources, quizzes, and the Student Profile chapters of the online classroom. If a student does not understand how to use these chapters of the classroom, please use the tutorials.

4. Start Discussion Question 1.
Week 2: Review of Random Variables
Learning Objective(s)
LO2.1 Identify discrete and continuous random variables and their functions (CO1).
LO2.2 Compute expected value and variance of random variables (CO1).
LO2.3 Explain the association between Random Variables and Stochastic Process in real world analysis
(CO2).

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 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.