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Probability and random variables for electrical engineering probability : measurement of uncertainty /

This book delivers a concise and carefully structured introduction to probability and random variables. It aims to build a linkage between the theoretical conceptual topics and the practical applications, especially in the undergraduate engineering area. The book motivates the student to gain full u...

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Main Author: Catak, Muammer,
Other Authors: Allahviranloo, Tofigh,, Pedrycz, Witold, 1953-, SpringerLink (Online service)
Format: eBook
Language: English
Published: Cham : Springer, [2022]
Physical Description: 1 online resource : illustrations (some color).
Series: Studies in systems, decision and control ; v. 390.
Subjects:
Probabilities.
Electrical engineering -- Mathematics.
Table of Contents:
  • Intro
  • Preface
  • Overview
  • Chapter Descriptions
  • Contents
  • Part I Concepts of Probability Theory
  • 1 Introduction
  • 1.1 Set Theory
  • 1.2 Set Operations
  • 1.3 Sample Space and Events
  • 1.4 Probability Axioms
  • 1.5 Probability of the Equally Likely Outcomes
  • 1.6 Conditional Probability and Bayes' Theory
  • 1.7 Problems
  • 2 Continuous Random Variables
  • 2.1 The Probability Distribution Function (PDF)
  • 2.2 The Probability Density Function (PDF)
  • 2.3 Expected Value and Variance
  • 2.4 Common Continuous Probability Distribution Functions
  • 2.4.1 Uniform Distribution.
  • 2.4.2 Normal (Gaussian) Distribution
  • 2.4.3 Exponential Distribution
  • 2.4.4 Gamma Distribution
  • 2.5 Problems
  • 3 Discrete Random Variables
  • 3.1 The Probability Distribution Function (PDF)
  • 3.2 The Probability Density Function (PDF)
  • 3.3 Expected Value and Variance
  • 3.4 Common Discrete Probability Distribution Functions
  • 3.4.1 Uniform Distribution
  • 3.4.2 Bernoulli Distribution
  • 3.4.3 Binomial Distribution
  • 3.4.4 Geometric Distribution
  • 3.4.5 The Memoryless Property of the Geometric Distribution
  • 3.4.6 Poisson Distribution
  • 3.5 The Mixed Probability Distributions.
  • 3.6 Problems
  • 4 Multiple Random Variables
  • 4.1 The Joint Probability Distribution Function
  • 4.2 The Joint Probability Density Function
  • 4.3 Marginal Probability Functions
  • 4.3.1 Marginal Probability Distribution Function
  • 4.3.2 Marginal Probability Density Function
  • 4.4 Conditional Probability and Statistical Independence
  • 4.5 Functions of Random Variables
  • 4.5.1 Y=aX+b, a>0, Continuous Random Variables
  • 4.5.2 Y=aX+b, a0, Discrete Random Variables
  • 4.5.4 Y=X2.
  • 4.5.5 Sum of Two Statistically Independent Continuous Random Variables, Z=X+Y
  • 4.5.6 Sum of Two Statistically Independent Discrete Random Variables, Z=X+Y
  • 4.5.7 Z=XY
  • 4.5.8 Z=XY
  • 4.5.9 Central Limit Theorem
  • 4.6 Problems
  • 5 Statistical Analysis of Random Variables
  • 5.1 Statistical Analysis of One Random Variable
  • 5.1.1 Expected Value and Mean
  • 5.1.2 Variance and Standard Deviation
  • 5.2 Moment Generating Functions
  • 5.2.1 Maclaurin Series
  • 5.2.2 Characteristic Function
  • 5.3 Statistical Analysis of Multiple Random Variables
  • 5.3.1 Normalized Joint Moments.
  • 5.3.2 Joint Moments Around the Expected Values
  • 5.3.3 Expected Operations of Functions of Random Variables
  • 5.4 Problems
  • Part II Random Processes
  • 6 Random Processes
  • 6.1 Random Processes
  • 6.1.1 Probability Functions Associated with a Random Process
  • 6.1.2 Classification of Random Processes
  • 6.2 Correlation Functions
  • 6.2.1 Autocorrelation Function, RXX(t1,t2)
  • 6.2.2 Cross-Correlation Function, RXY(t1,t2)
  • 6.3 Covariance Functions
  • 6.3.1 Autocovariance Function, CXX(t1,t2)
  • 6.3.2 Cross-covariance Function, CXX(t1,t2)
  • 6.4 Gaussian Random Process.

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