Librería Portfolio

Features

Presents the historical roots and applications of many theorems and definitions, accompanied by suitable examples or counterexamples
Provides the usual analytic proofs along with simple probabilistic arguments to promote a deeper understanding of the subject
Teaches students the preliminary concepts of probability before combinatorics, which makes the connection between the two areas clear from the beginning
Introduces the concepts of expectation and variance early so that students learn and use these important concepts as soon as possible
Emphasizes the Poisson distribution and processes
Incorporates a chapter on computer simulation, showing how to use algorithms to find approximate solutions to complicated probabilistic problems
Includes a collection of 1558 problems and exercises, with answers to the odd-numbered exercises at the back of the book
A solutions manual and figure slides are available upon qualifying course adoption.

Summary

Fundamentals of Probability with Stochastic Processes, Third Edition teaches probability in a natural way through interesting and instructive examples and exercises that motivate the theory, definitions, theorems, and methodology. The author takes a mathematically rigorous approach while closely adhering to the historical development of probability. He includes more than 1500 routine and challenging exercises, historical remarks, and discussions of probability problems recently published in journals, such as Mathematics Magazine and American Mathematical Monthly.

New to the Third Edition

Reorganized material to reflect a more natural order of topics
278 new exercises and examples as well as better solutions to the problems
New introductory chapter on stochastic processes
More practical, nontrivial applications of probability and stochastic processes in finance, economics, and actuarial sciences, along with more genetics examples
New section on survival analysis and hazard functions
More explanations and clarifying comments in almost every section
This versatile text is designed for a one- or two-term probability course for majors in mathematics, physical sciences, engineering, statistics, actuarial science, business and finance, operations research, and computer science. It also accessible to students who have completed a basic calculus course.



Table of Contents

Axioms of Probability
Introduction
Sample Space and Events
Axioms of Probability
Basic Theorems
Continuity of Probability Function
Probabilities 0 and 1
Random Selection of Points from Intervals
Review Problems

Combinatorial Methods
Introduction
Counting Principle
Permutations
Combinations
Stirling's Formula
Review Problems

Conditional Probability and Independence
Conditional Probability
Law of Multiplication
Law of Total Probability
Bayes' Formula
Independence
Applications of Probability to Genetics
Review Problems

Distribution Functions and Discrete Random Variables
Random Variables
Distribution Functions
Discrete Random Variables
Expectations of Discrete Random Variables
Variances and Moments of Discrete Random Variables
Standardized Random Variables
Review Problems

Special Discrete Distributions
Bernoulli and Binomial Random Variables
Poisson Random Variable
Other Discrete Random Variables
Review Problems

Continuous Random Variables
Probability Density Functions
Density Function of a Function of a Random Variable
Expectations and Variances
Review Problems

Special Continuous Distributions
Uniform Random Variable
Normal Random Variable
Exponential Random Variables
Gamma Distribution
Beta Distribution
Survival Analysis and Hazard Function
Review Problems

Bivariate Distributions
Joint Distribution of Two Random Variables
Independent Random Variables
Conditional Distributions
Transformations of Two Random Variables
Review Problems

Multivariate Distributions
Joint Distribution of n > 2 Random Variables
Order Statistics
Multinomial Distributions
Review Problems

More Expectations and Variances
Expected Values of Sums of Random Variables
Covariance
Correlation
Conditioning on Random Variables
Bivariate Normal Distribution
Review Problems

Sums of Independent Random Variables and Limit Theorems
Moment-Generating Functions
Sums of Independent Random Variables
Markov and Chebyshev Inequalities
Laws of Large Numbers
Central Limit Theorem
Review Problems

Stochastic Processes
Introduction
More on Poisson Processes
Markov Chains
Continuous-Time Markov Chains
Brownian Motion
Review Problems

Simulation
Introduction
Simulation of Combinatorial Problems
Simulation of Conditional Probabilities
Simulation of Random Variables
Monte Carlo Method

Appendix Tables

Answers to Odd-Numbered Exercises

Index