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Probability with STEM Applications, Third Edition, is an accessible and well-balanced introduction to post-calculus applied probability. Integrating foundational mathematical theory and the application of probability in the real world, this leading textbook engages students with unique problem scenarios and more than 1100 exercises of varying levels of difficulty. The text uses a hands-on, software-oriented approach to the subject of probability. MATLAB and R examples and exercises -- complemented by computer code that enables students to create their own simulations -- demonstrate the importance of software to solve problems that cannot be obtained analytically.
Revised and updated throughout, the textbook covers random variables and probability distributions, the basics of statistical inference, Markov chains, stochastic processes, signal processing, and more. This new edition is the perfect text for both year-long and single-semester mathematics and statistics courses, student engineers and scientists, and business and social science majors wanting to learn the quantitative aspects of their disciplines.
List of contents
Preface xv
Introduction 1
Why Study Probability? 1
Software Use in Probability 2
Modern Application of Classic Probability Problems 2
Applications to Business 3
Applications to the Life Sciences 4
Applications to Engineering and Operations Research 4
Applications to Finance 6
Probability in Everyday Life 7
1 Introduction to Probability 13
Introduction 13
1.1 Sample Spaces and Events 13
The Sample Space of an Experiment 13
Events 15
Some Relations from Set Theory 16
Exercises Section 1.1 (1-12) 18
1.2 Axioms Interpretations and Properties of Probability 19
Interpreting Probability 21
More Probability Properties 23
Contingency Tables 25
Determining Probabilities Systematically 26
Equally Likely Outcomes 27
Exercises Section 1.2 (13-30) 28
1.3 Counting Methods 30
The Fundamental Counting Principle 31
Tree Diagrams 32
Permutations 33
Combinations 34
Partitions 38
Exercises Section 1.3 (31-50) 39
Supplementary Exercises (51-62) 42
2 Conditional Probability and Independence 45
Introduction 45
2.1 Conditional Probability 45
The Definition of Conditional Probability 46
The Multiplication Rule for P(A intersection B) 49
Exercises Section 2.1 (1-16) 50
2.2 The Law of Total Probability and Bayes' Theorem 52
The Law of Total Probability 52
Bayes' Theorem 55
Exercises Section 2.2 (17-32) 59
2.3 Independence 61
The Multiplication Rule for Independent Events 63
Independence of More Than Two Events 65
Exercises Section 2.3 (33-54) 66
2.4 Simulation of Random Events 69
The Backbone of Simulation: Random Number Generators 70
Precision of Simulation 73
Exercises Section 2.4 (55-74) 74
Supplementary Exercises (75-100) 77
3 Discrete Probability Distributions: General Properties 82
Introduction 82
3.1 Random Variables 82
Two Types of Random Variables 84
Exercises Section 3.1 (1-10) 85
3.2 Probability Distributions for Discrete Random Variables 86
Another View of Probability Mass Functions 89
Exercises Section 3.2 (11-21) 90
3.3 The Cumulative Distribution Function 91
Exercises Section 3.3 (22-30) 95
3.4 Expected Value and Standard Deviation 96
The Expected Value of X 97
The Expected Value of a Function 99
The Variance and Standard Deviation of X 102
Properties of Variance 104
Exercises Section 3.4 (31-50) 105
3.5 Moments and Moment Generating Functions 108
The Moment Generating Function 109
Obtaining Moments from the MGF 111
Exercises Section 3.5 (51-64) 113
3.6 Simulation of Discrete Random Variables 114
Simulations Implemented in R and Matlab 117
Simulation Mean Standard Deviation and Precision 117
Exercises Section 3.6 (65-74) 119
Supplementary Exercises (75-84) 120
4 Families of Discrete Distributions 122
Introduction 122
4.1 Parameters and Families of Distributions 122
Exercises Section 4.1 (1-6) 124
4.2 The Binomial Distribution 125
The Binomial Random Variable and Distribution 127
Computing Binomial Probabilities 129
The Mean Variance and Moment Generating Function 130
B
Summary
Probability with STEM Applications, Third Edition, is an accessible and well-balanced introduction to post-calculus applied probability. Integrating foundational mathematical theory and the application of probability in the real world, this leading textbook engages students with unique problem scenarios and more than 1100 exercises of varying levels of difficulty. The text uses a hands-on, software-oriented approach to the subject of probability. MATLAB and R examples and exercises -- complemented by computer code that enables students to create their own simulations -- demonstrate the importance of software to solve problems that cannot be obtained analytically.
Revised and updated throughout, the textbook covers random variables and probability distributions, the basics of statistical inference, Markov chains, stochastic processes, signal processing, and more. This new edition is the perfect text for both year-long and single-semester mathematics and statistics courses, student engineers and scientists, and business and social science majors wanting to learn the quantitative aspects of their disciplines.
