# Probability-Random Variables and Stochastic Process

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## Probability-Random Variables and Stochastic Process PDF

PDF Name Probability-Random Variables and Stochastic Process October 18, 2022 eBooks United StatesGlobal 861 25.31 MB English ce.sharif.edu

## 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