Student’s Solutions Guide for Introduction to Probability, Statistics, and Random Processes

Book Preface

In this book, you will find guided solutions to the odd-numbered end-of-chapter problems found in the companion textbook, Introduction to Probability, Statistics, and Random Processes.
Since the textbook’s initial publication in 2014, I have received many requests to publish the solutions to those problems. I have published this book so that students may learn at their own pace with guided help through many of the problems presented in the original text.
It is my hope that this book serves its purpose well and enables students to access help to these problems. To access the original textbook as well as video lectures and probability calculators please visit www.probabilitycourse.com.

Acknowledgements
I would like to thank Laura Handly and Linnea Duley for their detailed review and comments. I am thankful to all of my teaching assistants who helped in various aspects of both the course and the book.

Contents
Preface v
1 Basic Concepts 1
2 Combinatorics: Counting Methods 27
3 Discrete Random Variables 39
4 Continuous and Mixed Random Variables 61
5 Joint Distributions: Two Random Variables 81
6 Multiple Random Variables 115
7 Limit Theorems and Convergence of RVs 133
8 Statistical Inference I: Classical Methods 143
9 Statistical Inference II: Bayesian Inference 157
10 Introduction to Random Processes 173
11 Some Important Random Processes 185
12 Introduction to Simulation Using MATLAB (Online) 205
13 Introduction to Simulation Using R (Online) 207
14 Recursive Methods 209