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.
Saeed Ghahramani is the dean of the College of Arts and Sciences and a professor of mathematics at Western New England University, Springfield, Massachusetts, USA. His research interests include chance and probability, higher education administration, and Persian poetry, culture, and language. He earned his Ph.D from the University of California, Berkeley, USA.
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