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

2.24

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

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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

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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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2.50

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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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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

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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

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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

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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

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

2.5 Independence of Events

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

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

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

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

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

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

2.6 Sequential Experiments

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

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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:

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

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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:

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

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

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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

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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

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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

2.118

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

2.119

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

2.9 *Fine Points: Probabilities of Sequences of Events

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

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

Problems Requiring Cumulative Knowledge

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

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

2.128

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

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