Introduction to Probability and Its Applications

ISBN-10: 0534386717
ISBN-13: 9780534386719
Edition: 3rd 2010 (Revised)
List price: $199.95 Buy it from $31.83 Rent it from $33.06
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Description: In this calculus-based text, theory is developed to a practical degree around models used in real-world applications. Proofs of theorems and "tricky" probability calculations are minimized. Computing and simulation are introduced to make more  More...

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Book details

List price: $199.95
Edition: 3rd
Copyright year: 2010
Publisher: Brooks/Cole
Publication date: 8/21/2009
Binding: Hardcover
Pages: 480
Size: 7.60" wide x 9.30" long x 0.90" tall
Weight: 3.916
Language: English

In this calculus-based text, theory is developed to a practical degree around models used in real-world applications. Proofs of theorems and "tricky" probability calculations are minimized. Computing and simulation are introduced to make more difficult problems accessible (although the material does not depend on the computer for continuity).

Richard L. Scheaffer, Professor Emeritus of Statistics, University of Florida, received his Ph.D. in statistics from Florida State University. Accompanying a career of teaching, research and administration, Dr. Scheaffer has led efforts on the improvement of statistics education throughout the school and college curriculum. Co-author of five textbooks, he was one of the developers of the Quantitative Literacy Project that formed the basis of the data analysis strand in the curriculum standards of the National Council of Teachers of Mathematics. He also led the task force that developed the AP Statistics Program, for which he served as Chief Faculty Consultant. Dr. Scheaffer is a Fellow and past president of the American Statistical Association, a past chair of the Conference Board of the Mathematical Sciences, and an advisor on numerous statistics education projects.

Linda J. Young, Ph.D., Oklahoma State University, is a Professor of Statistics at the University of Florida where she teaches, consults, and conducts research on statistical methods in public health, agricultural, environmental, and ecological settings. Dr. Young previously was a faculty member at Oklahoma State University and the University of Nebraska. Her more than 100 publications have appeared in 49 different journals, and was a recipient of the American Statistical Association's Founders Award. She has been editor of the Journal of Agricultural, Biological and Environmental Statistics and associate editor for Biometrics and Sequential Analysis. She has served as President of the Eastern North American Region of the American Statistical Association, Vice-President of the American Statistical Association, Chair of the Committee of Presidents of Statistical Societies, member of the National Institute of Statistical Science's Board of Directors, fellow of the American Statistical Association, and elected member of the International Statistical Institute. She has also served on numerous panels for the National Science Foundation and Environmental Protection Agency. Dr. Young's recent research has focused on linking disparate data sets and the subsequent analysis of these data using spatial statistical methods.

Probability in the World Around Us
Why Study Probability?
Deterministic and Probabilistic Models
Applications in Probability
A Brief Historical Note
A Look Ahead
Foundations of Probability
Randomness
Sample Space and Events
Definition of Probability
Counting Rules Useful in Probability
More Counting Rules Useful in Probability
Summary
Supplementary Exercises
Conditional Probability and Independence
Conditional Probability
Independence
Theorem of Total Probability and Bayes' Rule
Odds, Odds Rations, and Relative Risk
Summary
Supplementary Exercises
Discrete Probability Distributions
Random Variables and Their Probability Distributions
Expected Values of Random Variables
The Bernoulli Distribution
The Binomial Distribution
The Geometric Distribution
The Negative Binomial Distribution
The Poisson Distribution
The Hypergeometric Distribution
The Moment-Generating Function
The Probability-Generating Function
Markov Chains
Summary
Supplementary Exercises
Continuous Probability Distributions
Continuous Random Variables and Their Probability Distributions
Expected Values of Continuous Random Variables
The Uniform Distribution
The Exponential Distribution
The Gamma Distribution
The Normal Distribution
The Beta Distribution
The Weibull Distribution
Reliability
Moment-Generating Functions for Continuous Random Variables
Expectations of Discontinuous Functions and Mixed Probability Distributions
Summary
Supplementary Exercises
Multivariate Probability Distributions
Bivariate and Marginal Probability Distributions
Conditional Probability Distributions
Independent Random Variables
Expected Values of Functions of Random Variables
Conditional Expectations
The Multinomial Distribution
More on the Moment-Generating Function
Compounding and Its Applications
Summary
Supplementary Exercises
Functions of Random Variables
Introduction
Functions of Discrete Random Variables
Method of Distribution Functions
Method of Transformations in One Dimension
Method of Conditioning
Method of Moment-Generating Functions
Method of Transformation-Two Dimensions
Order Statistics
Probability-Generating Functions: Applications to Random Sums of Random Variables
Summary
Supplementary Exercises
Some Approximations to Probability Distributions: Limit Theorems
Introduction
Convergence in Probability
Convergence in Distributions
The Central Limit Theorem
Combination of Convergence in Probability and Convergence in Distributions
Summary
Supplementary Exercises
Extensions of Probability Theory
The Poisson Process
Birth and Death Processes: Biological Applications
Queues: Engineering Applications
Arrival Times for the Poisson Process
Infinite Server Queue
Renewal Theory: Reliability Applications
Summary
Appendix Tables
Answers to Selected Exercises
Index

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