Probability statistics and stochastic processes for engineers and scientists Cover Half Title Series Page Title Page Copyright Page Dedication Table of Contents Preface Authors Chapter 1 Preliminaries 1.1 Introduction 1.2 Set and Its Basic Properties 1.3 Zermelo and Fraenkel (ZFC) Axiomatic Set Theory 1.4 Basic Concepts of Measure Theory 1.5 Lebesgue Integral 1.6 Counting 1.7 Fuzzy Set Theory Fuzzy Logic and Fuzzy Measure Exercises Chapter 2 Basics of Probability 2.1 Basics of Probability 2.2 Fuzzy Probability 2.3 Conditional Probability 2.4 Independence 2.5 The Law of Total Probability and Bayes Theorem Exercises Chapter 3 Random Variables and Probability Distribution Functions 3.1 Introduction 3.2 Discrete Probability Distribution (Mass) Functions (pmf) 3.3 Moments of a Discrete Random Variable 3.3.1 Arithmetic Average 3.3.2 Moments of a Discrete Random Variable 3.4 Basic Standard Discrete Probability Mass Functions 3.4.1 Discrete Uniform pmf 3.4.2 Bernoulli pmf 3.4.3 Binomial pmf 3.4.4 Geometric pmf 3.4.5 Negative Binomial pmf 3.4.6 Hypergeometric pmf 3.4.7 Poisson pmf 3.5 Probability Distribution Function (cdf) for a Continuous Random Variable 3.6 Moments of a Continuous Random Variable 3.7 Continuous Moment Generating Function 3.8 Functions of Random Variables 3.9 Some Popular Continuous Probability Distribution Functions 3.9.1 Continuous Uniform Distribution 3.9.2 Gamma Distribution 3.9.3 Exponential Distribution 3.9.4 Beta Distribution 3.9.5 Erlang Distribution 3.9.6 Normal Distribution 3.9.7 χ[sup(2)] Chi Squared Distribution 3.9.8 The F Distribution 3.9.9 Students t Distribution 3.9.10 Weibull Distribution 3.9.11 Lognormal Distribution 3.9.12 Logistic Distribution 3.9.13 Extreme Value Distribution 3.10 Asymptotic Probabilistic Convergence.