Boncelet - Probability, Statistics, and Random Signals

Probability, Statistics, and Random Signals

Medium: Buch

ISBN: 978-0-19-020052-7

Verlag: Oxford University Press Inc

Erscheinungstermin: 20.02.2020

112,50 € 105,14 € (zzgl. MwSt.)

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- Preface

- 1 Probability Basics 1

- 1.1 What is Probability?

- 1.2 Experiments, Outcomes, and Events

- 1.3 Venn Diagrams

- 1.4 Random Variables

- 1.5 Basic Probability Rules

- 1.6 Probability Formalized

- 1.7 Little Theorems

- 1.8 Compound Experiments

- 1.9 Independence

- 1.10 Example: Can S CommunicateWith D?

- 1.10.1 List All Outcomes

- 1.10.2 Probability of a Union

- 1.10.3 Probability of the Complement

- 1.11 Example: Now Can S CommunicateWith D?

- 1.11.1 A Big Table

- 1.11.2 Break Into Pieces

- 1.11.3 Probability of the Complement

- 1.12 Computational Procedures

- 1.13 Summary

- 1.14 Problems

- 2 Conditional Probability 30

- 2.1 Definitions of Conditional Probability

- 2.2 Law of Total Probability and Bayes Theorem

- 2.3 Example: UrnModels

- 2.4 Example: A Binary Channel

- 2.5 Example: Drug Testing

- 2.6 Example: A Diamond Network

- 2.7 Summary

- 2.8 Problems

- 3 A Little Combinatorics 49

- 3.1 Basics of Counting

- 3.2 Notes on Computation

- 3.3 Combinations and the Binomial Coefficients

- 3.4 The Binomial Theorem

- 3.5 Multinomial Coefficient and Theorem

- 3.6 The Birthday Paradox andMessage Authentication

- 3.7 Hypergeometric Probabilities and Card Games

- 3.8 Summary

- 3.9 Problems

- 4 Discrete Probabilities and Random Variables

- 4.1 Discrete Random Variable and ProbabilityMass Functions

- 4.2 Cumulative Distribution Functions

- 4.3 Expected Values

- 4.4 Moment Generating Functions.

- 4.5 Several Important Discrete PMF’s

- 4.5.1 UniformPMF

- 4.5.2 Geometric ProbabilityMass Function (PMF)

- 4.5.3 The Poisson Distribution

- 4.6 Gambling and Financial DecisionMaking

- 4.7 Summary

- 4.8 Problems

- 5 Multiple Discrete Random Variables 110

- 5.1 Multiple Random Variables and PMFs

- 5.2 Independence

- 5.3 Moments and Expected Values

- 5.3.1 Expected Values for Two Random Variables

- 5.3.2 Moments for Two Random Variables

- 5.4 Example of Two Discrete Random Variables

- 5.4.1 Marginal PMFs and Expected Values

- 5.4.2 Independence

- 5.4.3 Joint Cumulative Distribution Function (CDF)

- 5.4.4 TransformationsWith One Output

- 5.4.5 TransformationsWith Several Outputs

- 5.4.6 Discussion

- 5.5 Sums of Independent Random Variables

- 5.6 Sample Probabilities,Mean, and Variance.

- 5.7 Histograms

- 5.8 Entropy and Data Compression

- 5.8.1 Entropy and Information Theory

- 5.8.2 Variable Length Coding

- 5.8.3 Encoding Binary Sequences.

- 5.8.4 MaximumEntropy

- 5.9 Summary

- 5.10 Problems

- 6 Binomial Probabilities

- 6.1 Basics of the Binomial Distribution

- 6.2 Computing Binomial Probabilities

- 6.3 Moments of the Binomial Distribution.

- 6.4 Sums of Independent Binomial Random Variables.

- 6.5 Distributions Related to the Binomial

- 6.5.1 Connections Between Binomial andHypergeometric Probabilities

- 6.5.2 Multinomial Probabilities.

- 6.5.3 Negative Binomial Distribution.

- 6.5.4 The Poisson Distribution

- 6.6 Parameter Estimation for Binomial andMultinomial Distributions

- 6.7 Alohanet

- 6.8 Error Control Codes.

- 6.8.1 Repetition by Three Code

- 6.8.2 General Linear Block Codes

- 6.8.3 Error Correcting Coding (ECC) Conclusions

- 6.9 Summary

- 6.10 Problems

- 7 A Continuous Random Variable

- 7.1 AContinuous Random Variable and Its Density,Distribution Function,

- and Expected Values.

- 7.2 Example Calculations for a Single Random Variable

- 7.3 Selected Continuous Distributions

- 7.3.1 The UniformDistribution

- 7.3.2 The Exponential Distribution

- 7.4 Conditional Probabilities for a Continuous Random Variable

- 7.5 Discrete PMF’s and Delta Functions

- 7.6 Quantization

- 7.7 Summary.

- 7.8 A FinalWord

- 7.9 Problems

- 8 Multiple Continuous Random Variables 206

- 8.1 Joint Densities and Distribution Functions

- 8.2 Expected Values andMoments

- 8.3 Independence

- 8.4 Conditional Probabilities forMultiple Random Variables

- 8.5 Extended Example of Two Continuous Random Variables

- 8.6 Sums of Independent Random Variables

- 8.7 Random Sums

- 8.8 General Transformations and the Jacobian

- 8.9 Parameter Estimation for the Exponential Distribution

- 8.10 Comparison of Discrete and Continuous Distributions

- 8.11 Summary

- 8.12 Problems

- 9 The Gaussian and Related Distributions

- 9.1 The Gaussian Distribution and Density

- 9.2 Quantile Function

- 9.3 Moments of the Gaussian Distribution

- 9.4 The Central Limit Theorem

- 9.5 Related Distributions

- 9.5.1 Laplace Distribution

- 9.5.2 Rayleigh Distribution

- 9.5.3 Chi-Squared and F Distributions

- 9.6 Multiple Gaussian RandomVariables.

- 9.6.1 Independent Gaussian Random Variables

- 9.6.2 Transformation to Polar Coordinates

- 9.6.3 Two Correlated Gaussians

- 9.7 Example: Digital Communications using QAM

- 9.7.1 Background

- 9.7.2 Discrete TimeModel

- 9.7.3 Monte Carlo Exercise

- 9.7.4 Quadrature AmplitudeModulation (QAM) Recap

- 9.8 Summary.

- 9.9 Problems

- 10 Elements of Statistics 282

- 10.1 A Simple Election Poll.

- 10.2 Estimating theMean and Variance.

- 10.3 Confidence Intervals

- 10.4 Recursive Calculation of the SampleMean.

- 10.5 ExponentialWeighting

- 10.6 Estimating the Distribution Function

- 10.7 PMF and Density Estimates

- 10.8 Order Statistics and Robust Estimates.

- 10.9 Significance Tests and P-Values

- 10.10Introduction to Estimation Theory

- 10.11MinimumMean Squared Error Estimation.

- 10.12Bayesian Estimation

- 10.13Problems

- 11 Gaussian Random Vectors and Linear Regression

- 11.1 Gaussian Random Vectors

- 11.2 Linear Operations on Gaussian Random Vectors

- 11.3 Linear Regression

- 11.3.1 Linear Regression in Detail.

- 11.3.2 Statistics of the Linear Regression Estimates.

- 11.3.3 Computational Issues

- 11.3.4 Linear Regression Examples.

- 11.3.5 Extensions of Linear Regression.

- 11.4 Summary.

- 11.5 Problems.

- 12 Hypothesis Testing

- 12.1 Hypothesis Testing: Basic Principles

- 12.2 Example of Radar Detection.

- 12.3 Hypothesis Tests and Likelihood Ratios

- 12.4 MaximumA Posteriori Tests

- 12.5 Summary.

- 12.6 Problems

- 13 Random Signals and Noise

- 13.1 Introduction to Random Signals

- 13.2 A Simple RandomProcess

- 13.3 Fourier Transforms.

- 13.4 Wide Sense Stationary RandomProcesses

- 13.5 Wide Sense Stationary (WSS) Signals and Linear Filters

- 13.6 Noise

- 13.6.1 Probabilistic Properties of Noise

-.

- 13.6.2 Spectral Properties of Noise

- 13.7 Example: AmplitudeModulation

- 13.8 The Sampling Theorem for WSS Random Processes

- 13.8.1 Discussion

- 13.8.2 Example: Figure 13.4.

- 13.8.3 Proof of Random Sampling Theorem

- 13.9 Summary

- 13.10 Problems

- 14 Selected Random Processes

- 14.1 A Lightbulb Process

- 14.2 A Poisson Process.

- 14.3 Markov Chains

- 14.4 Summary

- 14.5 Problems.

- A Computational Examples

- B Acronyms

- C Probability Tables

- C.1 Tables of Gaussian Probabilities.

- D Answers to Exercises

- Index

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