Probability, statistics, and stochastic processes

This book provides a unique and€balanced approach to probability, statistics, and stochastic processes. € Readers gain a solid foundation in all three fields that serves as a stepping stone to more advanced investigations into each area.€ The Second Edition features new coverage of analysis of variance (ANOVA), consistency and efficiency of estimators, asymptotic theory for maximum likelihood estimators, empirical distribution function and the Kolmogorov-Smirnov test, general linear models, multiple comparisons, Markov chain Monte Carlo (MCMC), Brownian motion, martingales, and.

6.3.1 Confidence Interval for the Mean in the Normal Distribution with Known Variance.

PROBABILITY, STATISTICS, AND STOCHASTIC PROCESSES; CONTENTS; Preface; Preface to the First Edition; 1 Basic Probability Theory; 1.1 Introduction; 1.2 Sample Spaces and Events; 1.3 The Axioms of Probability; 1.4 Finite Sample Spaces and Combinatorics; 1.4.1 Combinatorics; 1.5 Conditional Probability and Independence; 1.5.1 Independent Events; 1.6 The Law of Total Probability and Bayes' Formula; 1.6.1 Bayes' Formula; 1.6.2 Genetics and Probability; 1.6.3 Recursive Methods; Problems; 2 Random Variables; 2.1 Introduction; 2.2 Discrete Random Variables; 2.3 Continuous Random Variables.

2.3.1 The Uniform Distribution2.3.2 Functions of Random Variables; 2.4 Expected Value and Variance; 2.4.1 The Expected Value of a Function of a Random Variable; 2.4.2 Variance of a Random Variable; 2.5 Special Discrete Distributions; 2.5.1 Indicators; 2.5.2 The Binomial Distribution; 2.5.3 The Geometric Distribution; 2.5.4 The Poisson Distribution; 2.5.5 The Hypergeometric Distribution; 2.5.6 Describing Data Sets; 2.6 The Exponential Distribution; 2.7 The Normal Distribution; 2.8 Other Distributions; 2.8.1 The Lognormal Distribution; 2.8.2 The Gamma Distribution; 2.8.3 The Cauchy Distribution.

2.8.4 Mi…