Students Solutions Guide for Introduction to Probability, Statistics, and Random Processes (Hossein Pishro-Nik)— 2016 (Z-Library)

Student’s Solutions Guide for
Introduction to Probability, Statistics, and
Random Processes
Hossein Pishro-Nik
University of Massachusetts Amherst

Copyright c 2016 by Kappa Research, LLC. All rights reserved.
Published by Kappa Research, LLC.
No part of this publication may be reproduced in any form by any means, without
permission in writing from the publisher.
This book contains information obtained from authentic sources. Efforts have
been made to abide by the copyrights of all referenced and cited material con-
tained within this book.
The advice and strategies contained herein may not be suited for your individual
situation. As such, you should consult with a professional wherever appropri-
ate. This work is intended solely for the purpose of gaining understanding of the
principles and techniques used in solving problems of probability, statistics, and
random processes, and readers should exercise caution when applying these tech-
niques and methods to real-life situations. Neither the publisher nor the author
can be held liable for any loss of profit or any other commercial damages from
use of the contents of this text.
Printed in the United States of America
ISBN: 978-0-9906372-1-9

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
iii

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, Statis-
tics, 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 prob-
lems 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.
v