Book Title: A Self-Contained Course in Mathematical Theory of Probability

Book Description

This textbook is designed to be a self-contained read for STEM students to read who are taking a junior or senior level first course in mathematical statistics, such as the MA 412 course offered on Embry Riddle Aeronautical University’s Daytona Beach campus. Moreover, this text does not assume any formal perquisite knowledge in probability nor statistics, but it does assume that the student has completed a routine study of University calculus such as the common freshmen or sophomore math classes required in most engineering programs. This textbook originally began as an informal project of the authors during the COVID pandemic of 2020 designed as a tool to help students who were forced to suddenly shift from in person classroom learning to online learning. Then in the following year the University’s Center for Teaching and Learning Excellence sponsored a formal project under their textbook affordability initiative.  Now, for the content of the textbook most instructors would expect to start on Chapter 2. The first Chapter focuses on a brief review of introductory Data Analysis and it is expected that many students would have had some exposure to the Chapter 1 material in various advanced high school classwork; however, the reader who has not had any prior classwork in Statistics or Data Analysis it would be encouraged to fully study the Chapter 1. Then the Material in the remaining Chapters is fully self-contained. The Chapter 2 covers a brief summary of Discrete Probability. Then the Chapters 3 and 4 completes a full study of continuous Probability theory, ending with a general framework for the underlying mathematical theory of inferential statistics. The last Chapters is a unique chapter which connects the theory of Regression Modeling to the famous SIR model of disease spread; this later Chapter lead to many interesting student class research projects during the time of the COVID pandemic, and could be a jumping off point for students interested to further research related data and/or higher study in that field, but is not necessary to complete a junior or senior level first course in mathematical statistics, such as our MA 412 course.