Probability, Statistics, and Data Analysis

Alison Gibbs and Alex Stringer


Chapter 1 Introduction

This materials cover concepts from a traditional mathematical statistics course with less of a focus on theory and more on simulation and data analysis. They are designed to accompany or supplement such a course and were first used in STA238: Probability, Statistics and Data Analysis, Winter 2020 at the University of Toronto, taught by Alison Gibbs and Alex Stringer.

These notes are designed to stand alone, however the content pulls heavily from the following sources:

  • [MIPS] F.M. Dekking, C. Kraaikamp H.P. Lopuha ̈a and L.E. Meester (2005). A modern Introduction to Probability and Statistics: Understanding How and Why. Springer-Verlag. This is the primary reference for the course. This book is available in the University of Toronto bookstore. A pdf version of this textbook is freely available through the University of Toronto library website.

  • [E&R] M.J. Evans and J.S. Rosenthal (2003). Probability and Statistics: The Science of Uncertainty. W.H. Freeman and Co.Available in pdf here:

  • [ISL] G. James, D. Witten, T. Hastie and R. Tibshirani (2013). An Introduction to Statistical Learning with Applications in R. Springer. Available in pdf here:

Suggested practice problems from these sources are listed in the final chapter of these materials.

You can find the code used to create this book here. All of the data is stored in the data folder in this repository. You can look at the code for each chapter and copy bits and run them, though of course we recommend typing them out yourself!

Thanks and enjoy!

Alex Stringer, Alison Gibbs, and Sam Caetano