Introduction to Probability and Stochastic Processes with Applications

CONTENTS

Foreword

Preface

Acknowledgments

Introduction

1      Basic Concepts

  1.1      Probability Space

  1.2      Laplace Probability Space

  1.3      Conditional Probability and Event Independence

  1.4      Geometric Probability

Exercises

2      Random Variables and Their Distributions

  2.1      Definitions and Properties

  2.2      Discrete Random Variables

  2.3      Continuous Random Variables

  2.4      Distribution of a Function of a Random Variable

  2.5      Expected Value and Variance of a Random Variable

Exercises

3      Some Discrete Distributions

  3.1      Discrete Uniform, Binomial and Bernoulli Distributions

  3.2      Hypergeometric and Poisson Distributions

  3.3      Geometric and Negative Binomial Distributions

Exercises

4      Some Continuous Distributions

  4.1      Uniform Distribution

  4.2      Normal Distribution

  4.3      Family of Gamma Distributions

  4.4      Weibull Distribution

  4.5      Beta Distribution

  4.6      Other Continuous Distributions

Exercises

5      Random Vectors

  5.1      Joint Distribution of Random Variables

  5.2      Independent Random Variables

  5.3      Distribution of Functions of a Random Vector

  5.4      Covariance and Correlation Coefficient

  5.5      Expected Value of a Random Vector and Variance-Covariance Matrix

  5.6      Joint Probability Generating, Moment Generating and Characteristic Functions

Exercises

6      Conditional Expectation

  6.1      Conditional Distribution

  6.2      Conditional Expectation ...