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Produktbild: Probability and Random Processes with Applications to Signal Processing
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Probability and Random Processes with Applications to Signal Processing

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Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

03.06.2024

Verlag

Pearson Education Limited

Seitenzahl

704

Maße (L/B/H)

23,5/17,8/3,8 cm

Gewicht

1194 g

Auflage

4

Sprache

Englisch

ISBN

978-0-273-75228-8

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

03.06.2024

Verlag

Pearson Education Limited

Seitenzahl

704

Maße (L/B/H)

23,5/17,8/3,8 cm

Gewicht

1194 g

Auflage

4

Sprache

Englisch

ISBN

978-0-273-75228-8

Herstelleradresse


Email: info@bod.de

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  • Produktbild: Probability and Random Processes with Applications to Signal Processing

  • Preface

    1 Introduction to Probability 1

    1.1 Introduction: Why Study Probability? 1

    1.2 The Different Kinds of Probability 2

    Probability as Intuition 2

    Probability as the Ratio of Favorable to Total Outcomes (Classical Theory) 3

    Probability as a Measure of Frequency of Occurrence 4

    Probability Based on an Axiomatic Theory 5

    1.3 Misuses, Miscalculations, and Paradoxes in Probability 7

    1.4 Sets, Fields, and Events 8

    Examples of Sample Spaces 8

    1.5 Axiomatic Definition of Probability 15

    1.6 Joint, Conditional, and Total Probabilities; Independence 20

    Compound Experiments 23

    1.7 Bayes’ Theorem and Applications 35

    1.8 Combinatorics 38

    Occupancy Problems 42

    Extensions and Applications 46

    1.9 Bernoulli Trials–Binomial and Multinomial Probability Laws 48

    Multinomial Probability Law 54

    1.10 Asymptotic Behavior of the Binomial Law: The Poisson Law 57

    1.11 Normal Approximation to the Binomial Law 63

    Summary 65

    Problems 66

    References 77


     

    2 Random Variables 79

    2.1 Introduction 79

    2.2 Definition of a Random Variable 80

    2.3 Cumulative Distribution Function 83

    Properties of
    F
    X
    (
    x
    ) 84

    Computation of
    F
    X
    (
    x
    ) 85

    2.4 Probability Density Function (pdf) 88

    Four Other Common Density Functions 95

    More Advanced Density Functions 97

    2.5 Continuous, Discrete, and Mixed Random Variables 100

    Some Common Discrete Random Variables 102

    2.6 Conditional and Joint Distributions and Densities 107

    Properties of Joint CDF
    F
    XY
    (
    x, y
    ) 118

    2.7 Failure Rates 137

    Summary 141

    Problems 141

    References 149

    Additional Reading 149


     

    3 Functions of Random Variables 151

    3.1 Introduction 151

    Functions of a Random Variable (FRV): Several Views 154

    3.2 Solving Problems of the Type
    Y
    =
    g
    (
    X
    ) 155

    General Formula of Determining the pdf of
    Y
    =
    g
    (
    X
    ) 166

    3.3 Solving Problems of the Type
    Z
    =
    g
    (
    X, Y
    ) 171

    3.4 Solving Problems of the Type
    V
    =
    g
    (
    X, Y
    ),
    W
    =
    h
    (
    X, Y
    ) 193

    Fundamental Problem 193

    Obtaining
    f
    VW
    Directly from
    f
    XY
    196

    3.5 Additional Examples 200

    Summary 205

    Problems 206

    References 214

    Additional Reading 214


     

    4 Expectation and Moments 215

    4.1 Expected Value of a Random Variable 215

    On the Validity of Equation 4.1-8 218

    4.2 Conditional Expectations 232

    Conditional Expectation as a Random Variable 239

    4.3 Moments of Random Variables 242

    Joint Moments 246

    Properties of Uncorrelated Random Variables 248

    Jointly Gaussian Random Variables 251

    4.4 Chebyshev and Schwarz Inequalities 255

    Markov Inequality 257

    The Schwarz Inequality 258

    4.5 Moment-Generating Functions 261

    4.6 Chernoff Bound 264

    4.7 Characteristic Functions 266

    Joint Characteristic Functions 273

    The Central Limit Theorem 276

    4.8 Additional Examples 281

    Summary 283

    Problems 284

    References 293

    Additional Reading 294


     

    5 Random Vectors 295

    5.1 Joint Distribution and Densities 295

    5.2 Multiple Transformation of Random Variables 299

    5.3 Ordered Random Variables 302

    Distribution of area random variables 305

    5.4 Expectation Vectors and Covariance Matrices 311

    5.5 Properties of Covariance Matrices 314

    Whitening Transformation 318

    5.6 The Multidimensional Gaussian (Normal) Law 319

    5.7 Characteristic Functions of Random Vectors 328

    Properties of CF of Random Vectors 330

    The Characteristic