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Test Bank for Probability and Random Processes for Electrical and Computer Engineers (1st Edition)

By: John A. Gubner
ISBN-10: 0521864704
/ ISBN-13: 9780521864701

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Format: Downloadable ZIP Fille
Authors: John A. Gubner
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Description

Table of content:

Cover
Half Title
Title Page
Copyright
Dedication
Contents
Chapter dependencies
Preface
1. Introduction to probability
1.1 Sample spaces, outcomes, and events
1.2 Review of set notation
1.3 Probability models
1.4 Axioms and properties of probability
1.5 Conditional probability
1.6 Independence
1.7 Combinatorics and probability
Notes
Problems
Exam preparation
2. Introduction to discrete random variables
2.1 Probabilities involving random variables
2.2 Discrete random variables
2.3 Multiple random variables
2.4 Expectation
Notes
Problems
Exam preparation
3. More about discrete random variables
3.1 Probability generating functions
3.2 The binomial random variable
3.3 The weak law of large numbers
3.4 Conditional probability
3.5 Conditional expectation
Notes
Problems
Exam preparation
4. Continuous random variables
4.1 Densities and probabilities
4.2 Expectation of a single random variable
4.3 Transform methods
4.4 Expectation of multiple random variables
4.5 Probability bounds
Notes
Problems
Exam preparation
5. Cumulative distribution functions and their applications
5.1 Continuous random variables
5.2 Discrete random variables
5.3 Mixed random variables
5.4 Functions of random variables and their cdfs
5.5 Properties of cdfs
5.6 The central limit theorem
5.7 Reliability
Notes
Problems
Exam preparation
6. Statistics
6.1 Parameter estimators and their properties
6.2 Histograms
6.3 Confidence intervals for the mean – known variance
6.4 Confidence intervals for the mean – unknown variance
6.5 Confidence intervals for Gaussian data
6.6 Hypothesis tests for the mean
6.7 Regression and curve fitting
6.8 Monte Carlo estimation
Notes
Problems
Exam preparation
7. Bivariate random variables
7.1 Joint and marginal probabilities
7.2 Jointly continuous random variables
7.3 Conditional probability and expectation
7.4 The bivariate normal
7.5 Extension to three or more random variables
Notes
Problems
Exam preparation
8. Introduction to random vectors
8.1 Review of matrix operations
8.2 Random vectors and random matrices
8.3 Transformations of random vectors
8.4 Linear estimation of random vectors (Wiener filters)
8.5 Estimation of covariance matrices
8.6 Nonlinear estimation of random vectors
Notes
Problems
Exam preparation
9. Gaussian random vectors
9.1 Introduction
9.2 Definition of the multivariate Gaussian
9.3 Characteristic function
9.4 Density function
9.5 Conditional expectation and conditional probability
9.6 Complex random variables and vectors
Notes
Problems
Exam preparation
10. Introduction to random processes
10.1 Definition and examples
10.2 Characterization of random processes
10.3 Strict-sense and wide-sense stationary processes
10.4 WSS processes through LTI systems
10.5 Power spectral densities for WSS processes
10.6 Characterization of correlation functions
10.7 The matched filter
10.8 The Wiener filter
10.9 The Wiener–Khinchin theorem
10.10 Mean-square ergodic theorem for WSS processes
10.11 Power spectral densities for non-WSS processes
Notes
Problems
Exam preparation
11. Advanced concepts in random processes
11.1 The Poisson process
11.2 Renewal processes
11.3 The Wiener process
11.4 Specification of random processes
Notes
Problems
Exam preparation
12. Introduction to Markov chains
12.1 Preliminary results
12.2 Discrete-time Markov chains
12.3 Recurrent and transient states
12.4 Limiting n-step transition probabilities
12.5 Continuous-time Markov chains
Notes
Problems
Exam preparation
13. Mean convergence and applications
13.1 Convergence in mean of order p
13.2 Normed vector spaces of random variables
13.3 The Karhunen–Loève expansion
13.4 The Wiener integral (again)
13.5 Projections, orthogonality principle, projection theorem
13.6 Conditional expectation and probability
13.7 The spectral representation
Notes
Problems
Exam preparation
14. Other modes of convergence
14.1 Convergence in probability
14.2 Convergence in distribution
14.3 Almost-sure convergence
Notes
Problems
Exam preparation
15. Self similarity and long-range dependence
15.1 Self similarity in continuous time
15.2 Self similarity in discrete time
15.3 Asymptotic second-order self similarity
15.4 Long-range dependence
15.5 ARMA processes
15.6 ARIMA processes
Problems
Exam preparation
Bibliography
Index

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