Table of Contents

PREFACE
INTRODUCTION AND OVERVIEW
Making decisions under uncertainty
Overview of this book
PROBABILITY
Sample space, events, and probability
Rules of probability
Equally likely outcomes. Combinatorics
Conditional probability. Independence
DISCRETE RANDOM VARIABLES AND THEIR DISTRIBUTIONS
Distribution of a random variable
Distribution of a random vector
Expectation and variance
Families of discrete distributions
CONTINUOUS DISTRIBUTIONS
Probability density
Families of continuous distributions
Central limit theorem
COMPUTER SIMULATIONS AND MONTE CARLO METHODS
Introduction
Simulation of random variables
Solving problems by Monte Carlo methods
STOCHASTIC PROCESSES
Definitions and classifications
Markov processes and Markov chains
Counting processes
Simulation of stochastic processes
QUEUING SYSTEMS
Main components of a queuing system
The Little's Law
Bernoulli single-server queuing process
M/M/1 system
Multiserver queuing systems
Simulation of queuing systems
INTRODUCTION TO STATISTICS
Population and sample, parameters and statistics
Simple descriptive statistics
Graphical statistics
STATISTICAL INFERENCE
Parameter estimation
Confidence intervals
Unknown standard deviation
Hypothesis testing
Bayesian estimation and hypothesis testing
REGRESSION
Least squares estimation
Analysis of variance, prediction, and further inference
Multivariate regression
Model building
APPENDIX
Inventory of distributions
Distribution tables
Calculus review
Matrices and linear systems
Answers to selected exercises
Index