Buch, Englisch, 432 Seiten, Format (B × H): 190 mm x 234 mm, Gewicht: 668 g
Buch, Englisch, 432 Seiten, Format (B × H): 190 mm x 234 mm, Gewicht: 668 g
ISBN: 978-0-19-020052-7
Verlag: Oxford University Press Inc
Probability, Statistics, and Random Signals offers a comprehensive treatment of probability, giving equal treatment to discrete and continuous probability. The topic of statistics is presented as the application of probability to data analysis, not as a cookbook of statistical recipes. This student-friendly text features accessible descriptions and highly engaging exercises on topics like gambling, the birthday paradox, and financial decision-making.
Autoren/Hrsg.
Weitere Infos & Material
- 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
