This book was expanded from lecture materials I use in a one semester upper-division undergraduate course entitled Probability and Statistics at Youngstown State University. Those lecture materials, in turn, were based on notes that I transcribed as a graduate student at Bowling Green State University. The course for which the materials were written is 50-50 Probability and Statistics, and the attendees include mathematics, engineering, and computer science majors (among others). The catalog prerequisites for the course are a full year of calculus.

The book can be subdivided into three basic parts. The first part includes the introductions and elementary descriptive statistics; I want the students to be knee-deep in data right out of the gate. The second part is the study of probability, which begins at the basics of sets and the equally likely model, journeys past discrete/continuous random variables, and continues through to multivariate distributions. The chapter on sampling distributions paves the way to the third part, which is inferential statistics. This last part includes point and interval estimation, hypothesis testing, and finishes with introductions to selected topics in applied statistics.

I usually only have time in one semester to cover a small subset of this book. I cover the material in Chapter 2 in a class period that is supplemented by a take-home assignment for the students. I spend a lot of time on Data Description, Probability, Discrete, and Continuous Distributions. I mention selected facts from Multivariate Distributions in passing, and discuss the meaty parts of Sampling Distributions before moving right along to Estimation (which is another chapter I dwell on considerably). Hypothesis Testing goes faster after all of the previous work, and by that time the end of the semester is in sight. I normally choose one or two final chapters (sometimes three) from the remaining to survey, and regret at the end that I did not have the chance to cover more.

In an attempt to be correct I have included material in this book which I would normally not mention during the course of a standard lecture. For instance, I normally do not highlight the intricacies of measure theory or integrability conditions when speaking to the class. Moreover, I often stray from the matrix approach to multiple linear regression because many of my students have not yet been formally trained in linear algebra. That being said, it is important to me for the students to hold something in their hands which acknowledges the world of mathematics and statistics beyond the classroom, and which may be useful to them for many semesters to come. It also mirrors my own experience as a student.

The vision for this document is a more or less self contained, essentially complete, correct, introductory textbook.