# Probability, Random Variables and Stochastic Processes

```@inproceedings{Papoulis1965ProbabilityRV,
title={Probability, Random Variables and Stochastic Processes},
author={Athanasios Papoulis},
year={1965}
}```
Part 1 Probability and Random Variables 1 The Meaning of Probability 2 The Axioms of Probability 3 Repeated Trials 4 The Concept of a Random Variable 5 Functions of One Random Variable 6 Two Random Variables 7 Sequences of Random Variables 8 Statistics Part 2 Stochastic Processes 9 General Concepts 10 Random Walk and Other Applications 11 Spectral Representation 12 Spectral Estimation 13 Mean Square Estimation 14 Entropy 15 Markov Chains 16 Markov Processes and Queueing Theory
10,997 Citations

#### Topics from this paper

Elements of Probability Theory
• Mathematics
• 2013
This chapter presents a review of some basic concepts of probability theory, including probability spaces, random variables, random matrices, distributions, densities and expectations. Some classicalExpand
Time-Dependent Random Variables: Classical Stochastic Processes
If one considers a random variable which depends on time, one is led to the concept of a stochastic process. After the definition of a general stochastic process in Sect. 5.1, we introduce the classExpand
An Estimate of the Probability Density Function of the Sum of a Random Number N of Independent Random Variables
• Mathematics, Computer Science
• J. Comput. Eng.
• 2015
A new estimate of the probability density function (PDF) of the sum of a random number of independent and identically distributed (IID) random variables is shown. The sum PDF is represented as a sumExpand
Probability and Stochastic Processes
This chapter is an introduction to probability and statistics, providing basic definitions and properties related to probability theory and stochastic processes to help readers refresh their memoryExpand
Random Variables: Fundamentals of Probability Theory and Statistics
A fundamental concept for any statistical treatment is that of the random variable. Thus this concept and various other closely related ideas are presented at the beginning of this book. Section 2.1Expand
Probability, Random Variables, and Random Processes
The principal objective of this chapter is to introduce the basic concepts of probability, random variables, and random processes, with the sole focus of their applications in digital communications.Expand
Random Number and Variate Generation
• Mathematics
• 2013
This chapter discusses various methods for the generation of random samples distributed according to given probability distributions, in both the univariate and multivariate cases. These methods canExpand
On generating sets of binary random variables with specified first- and second- moments
• Computer Science, Mathematics
• Proceedings of the 2010 American Control Conference
• 2010
This work proposes a low-complexity algorithm for generating sets of binary random variables with specified means and pairwise correlations, and shows that the parameters of this data-generation algorithm can be easily designed to achieve the desired statistics, under broad conditions. Expand
On the Dimensionality of the Stochastic Space in the Stochastic Finite Element Method
In recent works concerning the solution of various kinds of random equations or the stochastic simulation of random functions often so called (generalized) polynomial chaos expansions are used.Expand
Random Variables : An Overview
This paper introduces the concept of a random variable, which is nothing more than a variable whose numeric value is determined by the outcome of an experiment. To describe the probabilities that areExpand

#### References

16-1 Introduction / 16-2 Markov Processes / 16-3 Queueing Theory / 16-4 Networks of Queues
• 16-1 Introduction / 16-2 Markov Processes / 16-3 Queueing Theory / 16-4 Networks of Queues