Instructor’s Solutions Manual 2-1 Probability, Statistics, and Random Processes for Electrical Engineers

Chapter 2: Basic Concepts of Probability Theory

2.1 Specifying Random Experiments

2.1

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Instructor’s Solutions Manual 2-2 Probability, Statistics, and Random Processes for Electrical Engineers

2.2

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Instructor’s Solutions Manual 2-3 Probability, Statistics, and Random Processes for Electrical Engineers

2.3

2.4

2.5

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Instructor’s Solutions Manual 2-4 Probability, Statistics, and Random Processes for Electrical Engineers

2.6

2.7

2.8

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Instructor’s Solutions Manual 2-5 Probability, Statistics, and Random Processes for Electrical Engineers

2.9

2.10

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Instructor’s Solutions Manual 2-6 Probability, Statistics, and Random Processes for Electrical Engineers

2.11

2.12

2.13

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Instructor’s Solutions Manual 2-7 Probability, Statistics, and Random Processes for Electrical Engineers

2.14

2.15

2.16

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Instructor’s Solutions Manual 2-8 Probability, Statistics, and Random Processes for Electrical Engineers

2.17

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Instructor’s Solutions Manual 2-9 Probability, Statistics, and Random Processes for Electrical Engineers

2.18

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Instructor’s Solutions Manual 2-10 Probability, Statistics, and Random Processes for Electrical Engineers

2.19

2.20

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Instructor’s Solutions Manual 2-11 Probability, Statistics, and Random Processes for Electrical Engineers

2.2 The Axioms of Probability

2.21

2.22

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Instructor’s Solutions Manual 2-12 Probability, Statistics, and Random Processes for Electrical Engineers

2.26

2.25

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2.23

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Instructor’s Solutions Manual 2-13 Probability, Statistics, and Random Processes for Electrical Engineers

2.27

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Instructor’s Solutions Manual 2-14 Probability, Statistics, and Random Processes for Electrical Engineers

2.28

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Instructor’s Solutions Manual 2-15 Probability, Statistics, and Random Processes for Electrical Engineers

2.29

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Instructor’s Solutions Manual 2-16 Probability, Statistics, and Random Processes for Electrical Engineers

2.30

(c)

2.31

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Instructor’s Solutions Manual 2-17 Probability, Statistics, and Random Processes for Electrical Engineers

2.32

2.33

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Instructor’s Solutions Manual 2-18 Probability, Statistics, and Random Processes for Electrical Engineers

2.34

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Instructor’s Solutions Manual 2-19 Probability, Statistics, and Random Processes for Electrical Engineers

2.35

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Instructor’s Solutions Manual 2-20 Probability, Statistics, and Random Processes for Electrical Engineers

2.36

2.37

2.38

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Instructor’s Solutions Manual 2-21 Probability, Statistics, and Random Processes for Electrical Engineers

2.3 *Computing Probabilities Using Counting Methods

2.39

2.40

2.41

2.42

2.43

2.44

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Instructor’s Solutions Manual 2-22 Probability, Statistics, and Random Processes for Electrical Engineers

2.45

2.46

2.47

2.48

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Instructor’s Solutions Manual 2-23 Probability, Statistics, and Random Processes for Electrical Engineers

2.49

2.53

2.52

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Instructor’s Solutions Manual 2-24 Probability, Statistics, and Random Processes for Electrical Engineers

2.55

2.54a

(b)

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Instructor’s Solutions Manual 2-25 Probability, Statistics, and Random Processes for Electrical Engineers

2.58

2.57

2.56

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Instructor’s Solutions Manual 2-26 Probability, Statistics, and Random Processes for Electrical Engineers

2.59

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2.61

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Instructor’s Solutions Manual 2-27 Probability, Statistics, and Random Processes for Electrical Engineers

2.4 Conditional Probability

2.63a

2.62

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Instructor’s Solutions Manual 2-28 Probability, Statistics, and Random Processes for Electrical Engineers

2.64

2.63c

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Instructor’s Solutions Manual 2-29 Probability, Statistics, and Random Processes for Electrical Engineers

2.65

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2.66

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Instructor’s Solutions Manual 2-30 Probability, Statistics, and Random Processes for Electrical Engineers

2.68

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Instructor’s Solutions Manual 2-31 Probability, Statistics, and Random Processes for Electrical Engineers

2.70

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Instructor’s Solutions Manual 2-32 Probability, Statistics, and Random Processes for Electrical Engineers

2.72

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Instructor’s Solutions Manual 2-33 Probability, Statistics, and Random Processes for Electrical Engineers

2.73

2.74

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Instructor’s Solutions Manual 2-34 Probability, Statistics, and Random Processes for Electrical Engineers

2.75

2.76

(b)

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Instructor’s Solutions Manual 2-35 Probability, Statistics, and Random Processes for Electrical Engineers

2.77

2.78

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Instructor’s Solutions Manual 2-36 Probability, Statistics, and Random Processes for Electrical Engineers

2.79

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Instructor’s Solutions Manual 2-37 Probability, Statistics, and Random Processes for Electrical Engineers

2.80

2.81

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Instructor’s Solutions Manual 2-38 Probability, Statistics, and Random Processes for Electrical Engineers

2.5 Independence of Events

2.84

2.83

2.82

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Instructor’s Solutions Manual 2-39 Probability, Statistics, and Random Processes for Electrical Engineers

2.85

2.86

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Instructor’s Solutions Manual 2-40 Probability, Statistics, and Random Processes for Electrical Engineers

2.87

2.88

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Instructor’s Solutions Manual 2-41 Probability, Statistics, and Random Processes for Electrical Engineers

2.89

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2.91

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Instructor’s Solutions Manual 2-42 Probability, Statistics, and Random Processes for Electrical Engineers

2.92

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Instructor’s Solutions Manual 2-43 Probability, Statistics, and Random Processes for Electrical Engineers

2.95

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Instructor’s Solutions Manual 2-44 Probability, Statistics, and Random Processes for Electrical Engineers

2.6 Sequential Experiments

2.97

2.98

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Instructor’s Solutions Manual 2-45 Probability, Statistics, and Random Processes for Electrical Engineers

2.99

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Instructor’s Solutions Manual 2-46 Probability, Statistics, and Random Processes for Electrical Engineers

2.102

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Instructor’s Solutions Manual 2-47 Probability, Statistics, and Random Processes for Electrical Engineers

2.104

2.105

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Instructor’s Solutions Manual 2-48 Probability, Statistics, and Random Processes for Electrical Engineers

2.106

2.107

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Instructor’s Solutions Manual 2-49 Probability, Statistics, and Random Processes for Electrical Engineers

2.108

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Instructor’s Solutions Manual 2-50 Probability, Statistics, and Random Processes for Electrical Engineers

2.7 *Synthesizing Randomness: Random Number Generators

2.109

2.110

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Instructor’s Solutions Manual 2-51 Probability, Statistics, and Random Processes for Electrical Engineers

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Instructor’s Solutions Manual 2-52 Probability, Statistics, and Random Processes for Electrical Engineers

2.113

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Instructor’s Solutions Manual 2-53 Probability, Statistics, and Random Processes for Electrical Engineers

2.114

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Instructor’s Solutions Manual 2-54 Probability, Statistics, and Random Processes for Electrical Engineers

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Instructor’s Solutions Manual 2-55 Probability, Statistics, and Random Processes for Electrical Engineers

2.8 *Fine Points: Event Classes

2.117

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Instructor’s Solutions Manual 2-56 Probability, Statistics, and Random Processes for Electrical Engineers

(d)

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Instructor’s Solutions Manual 2-57 Probability, Statistics, and Random Processes for Electrical Engineers

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Instructor’s Solutions Manual 2-58 Probability, Statistics, and Random Processes for Electrical Engineers

2.119

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Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.

Instructor’s Solutions Manual 2-59 Probability, Statistics, and Random Processes for Electrical Engineers

2.9 *Fine Points: Probabilities of Sequences of Events

2.120

2.121

2.122

© 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.This material is is protected by Copyright and written permission

should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to:

Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.

Instructor’s Solutions Manual 2-60 Probability, Statistics, and Random Processes for Electrical Engineers

2.123

2.124

© 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.This material is is protected by Copyright and written permission

should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to:

Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.

Instructor’s Solutions Manual 2-61 Probability, Statistics, and Random Processes for Electrical Engineers

Problems Requiring Cumulative Knowledge

2.125

© 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.This material is is protected by Copyright and written permission

should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to:

Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.

Instructor’s Solutions Manual 2-62 Probability, Statistics, and Random Processes for Electrical Engineers

2.126

2.127

© 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.This material is is protected by Copyright and written permission

should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to:

Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.

Instructor’s Solutions Manual 2-63 Probability, Statistics, and Random Processes for Electrical Engineers

2.128

© 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.This material is is protected by Copyright and written permission

should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to:

Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.

Instructor’s Solutions Manual 2-64 Probability, Statistics, and Random Processes for Electrical Engineers

© 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.This material is is protected by Copyright and written permission

should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to:

Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.