Instructor Solution Manual
Probability and Statistics for Engineers and Scientists
(3rd Edition)
Anthony Hayter
, 1
Instructor Solution Manual
This instructor solution manual to accompany the third edition of
“Probability and Statistics for Engineers and Scientists” by Anthony Hayter
provides worked solutions and answers to all of the problems given in the textbook. The student
solution manual provides worked solutions and answers to only the odd-numbered problems
given at the end of the chapter sections. In addition to the material contained in the student
solution manual, this instructor manual therefore provides worked solutions and answers to
the even-numbered problems given at the end of the chapter sections together with all of the
supplementary problems at the end of each chapter.
,2
, Contents
1 Probability Theory 7
1.1 Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2 Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3 Combinations of Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.4 Conditional Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.5 Probabilities of Event Intersections . . . . . . . . . . . . . . . . . . . . . . . . . . 22
1.6 Posterior Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
1.7 Counting Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
1.9 Supplementary Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2 Random Variables 49
2.1 Discrete Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.2 Continuous Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.3 The Expectation of a Random Variable . . . . . . . . . . . . . . . . . . . . . . . 58
2.4 The Variance of a Random Variable . . . . . . . . . . . . . . . . . . . . . . . . . 62
2.5 Jointly Distributed Random Variables . . . . . . . . . . . . . . . . . . . . . . . . 68
2.6 Combinations and Functions of Random variables . . . . . . . . . . . . . . . . . . 77
2.8 Supplementary Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
3 Discrete Probability Distributions 95
3.1 The Binomial Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
3.2 The Geometric and Negative Binomial Distributions . . . . . . . . . . . . . . . . 99
3.3 The Hypergeometric Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
3.4 The Poisson Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
3.5 The Multinomial Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
3.7 Supplementary Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
4 Continuous Probability Distributions 113
4.1 The Uniform Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
4.2 The Exponential Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
4.3 The Gamma Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.4 The Weibull Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
4.5 The Beta Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
4.7 Supplementary Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
3
Probability and Statistics for Engineers and Scientists
(3rd Edition)
Anthony Hayter
, 1
Instructor Solution Manual
This instructor solution manual to accompany the third edition of
“Probability and Statistics for Engineers and Scientists” by Anthony Hayter
provides worked solutions and answers to all of the problems given in the textbook. The student
solution manual provides worked solutions and answers to only the odd-numbered problems
given at the end of the chapter sections. In addition to the material contained in the student
solution manual, this instructor manual therefore provides worked solutions and answers to
the even-numbered problems given at the end of the chapter sections together with all of the
supplementary problems at the end of each chapter.
,2
, Contents
1 Probability Theory 7
1.1 Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2 Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3 Combinations of Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.4 Conditional Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.5 Probabilities of Event Intersections . . . . . . . . . . . . . . . . . . . . . . . . . . 22
1.6 Posterior Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
1.7 Counting Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
1.9 Supplementary Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2 Random Variables 49
2.1 Discrete Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.2 Continuous Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.3 The Expectation of a Random Variable . . . . . . . . . . . . . . . . . . . . . . . 58
2.4 The Variance of a Random Variable . . . . . . . . . . . . . . . . . . . . . . . . . 62
2.5 Jointly Distributed Random Variables . . . . . . . . . . . . . . . . . . . . . . . . 68
2.6 Combinations and Functions of Random variables . . . . . . . . . . . . . . . . . . 77
2.8 Supplementary Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
3 Discrete Probability Distributions 95
3.1 The Binomial Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
3.2 The Geometric and Negative Binomial Distributions . . . . . . . . . . . . . . . . 99
3.3 The Hypergeometric Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
3.4 The Poisson Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
3.5 The Multinomial Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
3.7 Supplementary Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
4 Continuous Probability Distributions 113
4.1 The Uniform Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
4.2 The Exponential Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
4.3 The Gamma Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.4 The Weibull Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
4.5 The Beta Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
4.7 Supplementary Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
3
