Fundamentals of Probability
Chapman & Hall/CRC (Verlag)
978-1-4987-5501-6 (ISBN)
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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
| Erscheinungsdatum | 30.01.2016 |
|---|---|
| Zusatzinfo | 23 Tables, black and white; 68 Illustrations, black and white |
| Verlagsort | Philadelphia, PA |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 1293 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik |
| ISBN-10 | 1-4987-5501-1 / 1498755011 |
| ISBN-13 | 978-1-4987-5501-6 / 9781498755016 |
| Zustand | Neuware |
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