Probability-Random Variables and Stochastic Process

Probability-Random Variables and Stochastic Process PDF - Overview

Probability-Random Variables and Stochastic Process – It is Fourth edition of Probability-Random Variables and Stochastic Process. Stochastic processes are probabilistic models for random quantities evolving in time or space. The evolution is governed by some dependence relationship between the random quantities at different times or locations.

In probability theory and related fields, a stochastic or random process is a mathematical object usually defined as a family of random variables. Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner.

Some basic types of stochastic processes include Markov processes, Poisson processes (such as radioactive decay), and time series, with the index variable referring to time. This indexing can be either discrete or continuous, the interest being in the nature of changes of the variables with respect to time.

Probability-Random Variables and Stochastic Process

Contents of Probability-Random Variables, and Stochastic Process

Preface

Probability-Random Variables and Stochastic Process – Part 1 – Probability And Random Variables

• Chapter – 1 The Meaning Of Probability
  Introduction
  The Definitions
  Probability And Induction
  Causality Versus Randomness
• Chapter – 2 The Axioms Of Probability
  Set Theory
  Probability Space
  Conditional Probability
  Problems
• Chapter – 3 Repeated Trials
  Combined Experiments
  Bernoulli Trials
  Bernoulli’s Theorem And Games Of Chance
  Problems
• Chapter – 4 The Concept Of A Random Variable
  Introduction
  Distribution And Density Functions
  Specific Random Variables
  Conditional Distributions
  Asymptotic Approximations For Binomial Random Variable
  Problems
• Chapter – 5 Functions Of One Random Variable
  The Random Variable G(X)
  The Distribution ” Of G(X)
  Mean And Variance Moments
  Characteristic Functions
  Problems
• Chapter – 6 Two Random Variables
  Bivariate Distributions
  One Function Of Two Random Variables
  Two Functions Of Two Random Variables
  Joint Moments
  Joint Characteristic Functions
  Conditional Distributions
  Conditional Expected Values
  Problems
• Chapter – 7 Sequences Of Random ‘Variables
  General Concepts
  Conditional Densities, Characteristic Functions, And Normality
  M~ Square Estimation
  Stochastic Convergence And Limit Theorems
  Random Numbers: Meaning And Generation
  Problems
• Chapter – 8 Statistics
  Introduction
  Estimation
  Parameter Estimation
  Hypothesis Testing
  Problems

Probability-Random Variables and Stochastic Process – Part – 2 Stochastic Processes

• Chapter – 9 General Concepts
  Definitions
  Systems With Stochastic Inputs
  The Power Spectrum
  Discrete-Time Processes
  Appendix 9a Continuity, Differentiation, Integration
  Appendix 9b Shift Operators And Stationary Processes
  Problems
• Chapter – 10 Random Walks And Other Applications
  Random Walks
  Poisson Points And Shot Noise
  Modulation
  Cyclostationary Processes
  Bandlimited Processes And Sampling Theory
  Deterministic Signals In Noise
  Bispectra And System Identification
  Appendix Loa The Poisson Sum Formula
  Appendix Lob The Schwarz Inequality
  Problems
• Chapter – 11 Spectral Representation
  Factorization And Innovations
  Finite-Order Systems And State Variables
  Fourier Series And Karhunen-Loeve Expansions
  Spectral Representation Of Random Processes
  Problems
• Chapter – 12 Spectrum Estimation
  Ergodicity
  Spectrum Estimation
  Extrapolation And System Identification
  The General Class Of Extrapolating Spectra And Youla’s Parametrization
  Appendix 12a Minimum-Phase Functions
  Appendix 12b All-Pass Functions
  Problems
• Chapter – 13 Mean Square Estimation
  Introduction
  Prediction
  Filtering And Prediction
  Kalman Filters
  Problems
• Chapter – 14 Entropy
  Introduction
  Basic Concepts
  Random Variables And Stochastic Processes
  The Maximum Entropy Method Coding
  Channel Capacity
  Problems
• Chapter – 15 Markov Chains
  Introduction
  Higher Transition Probabilities And The Chapman-Kolmogorov Equation
  Classification Of Stales
  Stationary Distributions And Limiting Probabilities
  Transient States And Absorption Probabilities
  Branching Processes
  Appendix 15a Mixed Type Population Of Constant Size
  Appendix 15b Structure Of Periodic Chains
  Problems
• Chapter – 16 Markov Processes And Queueing Theory
  Introduction
  Markov Processes
  Queueing Theory
  Networks Of Queues
  Problems
• Bibliography
• Index

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