# Probability, Random Signals, and Statistics

## 1st Edition

CRC Press

472 pages

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### Description

With this innovative text, the study-and teaching- of probability and random signals becomes simpler, more streamlined, and more effective. Its unique "textgraph" format makes it both student-friendly and instructor-friendly. Pages with a larger typeface form a concise text for basic topics and make ideal transparencies; pages with smaller type provide more detailed explanations and more advanced material.

INTRODUCTION

Randomness, Random Signals and Systems

Probability and Random Processes

Typical Engineering Applications

Why Study Probability and Random Signals

Key Features of the Book

Rules for the Presentation

BASIC CONCEPTS IN PROBABILITY

Basics of Set Theory

Fundamental Concepts in Probability

Conditional Probability

Independent Events

Total Probability Theorem and Bayes' Rule

Combined Experiments and Bernoulli Trials

THE RANDOM VARIABLE

Concept of Random Variable

Cumulative Distribution Function

Probability Density Function

Uniform Distribution

Gaussian Distribution and Central Limit Theorem

Some Other Commonly Used Distributions

Expectation and Moments

Functions of a Random Variable

Conditional Distributions

Generation of Random Numbers

Determination of Distribution from Data

Characteristic Functions

MULTIPLE RANDOM VARIABLES

Joint Distribution Functions

Joint Density Function

Independence of Random Variables

Expectation and Moments

Relation between Two Random Variables

Uniform Distributions

Jointly Gaussian Random Variables

Functions of Random Variables

Conditional Distributions

INTRODUCTION TO STATISTICS

Introduction

Sample Mean and Sample Variance

Empirical Distributions

Statistical Inference

Parameter Estimation

Hypothesis Testing

Linear Regression and Curve Fitting

RANDOM PROCESSES

Concept of Random Process

Characterization of Random Processes

Classification of Random Processes

Correlation Functions

Properties of Autocorrelation Functions

Sample Mean and Sample Correlation Functions

Relationship between Two Random Processes

Properties of Crosscorrelation Functions

Gaussian Random Processes

POWER SPECTRAL DENSITY

Concept of Power Spectral Density

Properties of Power Spectral Density

White Noise

Power Spectrum Estimation

Cross-Power Spectrum

Power Spectrum in Laplace Domain

Some Facts about Fourier Transforms

LINEAR SYSTEMS WITH RANDOM INPUTS

Deterministic Linear Systems

Time-Domain Analysis

Frequency-Domain Analysis

Summary of Input-Output Relationships

Linear Systems with White Noise Input

Equivalent Noise Bandwidth

Output of a Linear System as a Gaussian Process

OPTIMAL LINEAR SYSTEMS

Introduction

Signal-to-Noise Ratio

The Matched Filter

The Wiener Filter

Plus each chapter includes a summary, additional examples, problems, computer exercises, and self-test problems with solutions.

### Subject Categories

##### BISAC Subject Codes/Headings:
MAT029000
MATHEMATICS / Probability & Statistics / General
TEC007000
TECHNOLOGY & ENGINEERING / Electrical