Solucionario De Probability Statistics And Random Processes For Electrical Engineering - Leon-Garcia A.

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Section Mathematical Models as Tools in Analysis and Design
Section Deterministic Models
Section Probability Models
Section A Detailed Example: A Packet Voice Transmission System
Section Other Examples
Section Overview of Book

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Section Specifying Random Experiments
Section The Axioms of Probability
Section Computing Probabilities Using Counting Methods
Section Conditional Probability
Section Independence of Events
Section Sequential Experiments
Section Synthesizing Randomness: Random Number Generators
Section Fine Points: Event Classes
Section Fine Points: Probabilities of Sequences of Events

Section The Notion of a Random Variable
Section Discrete Random Variables and Probability Mass Function
Section Expected Value and Moments of Discrete Random Variable
Section Conditional Probability Mass Function
Section Important Discrete Random Variables
Section Generation of Discrete Random Variables

Section The Cumulative Distribution Function
Section The Probability Density Function
Section The Expected Value of X
Section Important Continuous Random Variables
Section Functions of a Random Variable
Section The Markov and Chebyshev Inequalities
Section Transform Methods
Section Basic Reliability Calculations
Section Computer Methods for Generating Random Variables
Section Entropy

Section Two Random Variables
Section Pairs of Discrete Random Variables
Section The Joint cdf of X and Y
Section The Joint pdf of Two Continuous Random Variables
Section Independence of Two Random Variables
Section Joint Moments and Expected Values of a Function of Two Random Variables
Section Conditional Probability and Conditional Expectation
Section Functions of Two Random Variables
Section Pairs of Jointly Gaussian Random Variables
Section Generating Independent Gaussian Random Variables

Section Vector Random Variables
Section Functions of Several Random Variables
Section Expected Values of Vector Random Variables
Section Jointly Gaussian Random Vectors
Section Estimation of Random Variables
Section Generating Correlated Vector Random Variables

Section Sums of Random Variables
Section The Sample Mean and the Laws of Large Numbers
Section The Central Limit Theorem
Section Convergence of Sequences of Random Variables
Section Long-Term Arrival Rates and Associated Averages
Section Calculating Distribution’s Using the Discrete Fourier Transform

Section Samples and Sampling Distributions
Section Parameter Estimation
Section Maximum Likelihood Estimation
Section Confidence Intervals
Section Hypothesis Testing
Section Bayesian Decision Methods
Section Testing the Fit of a Distribution to Data

Section Definition of a Random Process
Section Specifying a Random Process
Section Discrete-Time Processes: Sum Process, Binomial Counting Process, and Random Walk
Section Poisson and Associated Random Processes
Section Gaussian Random Processes, Wiener Process and Brownian Motion
Section Stationary Random Processes
Section Continuity, Derivatives, and Integrals of Random Processes
Section Time Averages of Random Processes and Ergodic Theorems
Section Fourier Series and Karhunen-Loeve Expansion
Section Generating Random Processes

Section Power Spectral Density
Section Response of Linear Systems to Random Signals
Section Bandlimited Random Processes
Section Optimum Linear Systems
Section The Kalman Filter
Section Estimating the Power Spectral Density
Section Numerical Techniques for Processing Random Signals

Section Markov Processes
Section Discrete-Time Markov Chains
Section Classes of States, Recurrence Properties, and Limiting Probabilities
Section Continuous-Time Markov Chains
Section Time-Reversed Markov Chains
Section Numerical Techniques for Markov Chains

Section The Elements of a Queueing System
Section Little’s Formula
Section The M/M/1 Queue
Section Multi-Server Systems: M/M/c, M/M/c/c, And M/M/&#8734
Section Finite-Source Queueing Systems
Section M/G/1 Queueing Systems
Section M/G/1 Analysis Using Embedded Markov Chains
Section Burke’s Theorem: Departures From M/M/c Systems
Section Networks of Queues: Jackson’s Theorem
Section Simulation and Data Analysis of Queueing Systems

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La comprensión profunda de la probabilidad, la estadística y los procesos aleatorios es un componente esencial en la formación del ingeniero eléctrico moderno. En un entorno cada vez más regido por señales digitales, comunicación inalámbrica, sistemas embebidos, redes de sensores, procesamiento de imágenes y control automático, la presencia de incertidumbre es inherente a los datos, las mediciones y los sistemas físicos. Afrontar este grado de complejidad requiere herramientas matemáticas robustas que permitan modelar, analizar y diseñar soluciones eficaces en presencia de variabilidad y ruido. La teoría de la probabilidad proporciona el marco formal para representar y razonar sobre la incertidumbre. Al introducir los conceptos de espacio muestral, eventos, axiomas de probabilidad, y reglas de combinación, se establece una base lógica que permite describir fenómenos aleatorios y predecir su comportamiento a través del cálculo de probabilidades. Este enfoque es fundamental para analizar errores en transmisiones, variaciones en componentes electrónicos, fluctuaciones en señales, o eventos discretos en redes de telecomunicaciones.