First Course in Probability

ISBN-10: 0130338516
ISBN-13: 9780130338518
Edition: 6th 2002
Authors: Sheldon Ross
List price: $106.67
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Description: This introduction to probability features clear explanations of the mathematics of probability theory and explores its many diverse applications through numerous motivational examples.

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Book details

List price: $106.67
Edition: 6th
Copyright year: 2002
Publisher: Prentice Hall PTR
Publication date: 7/31/2001
Binding: Hardcover
Pages: 528
Size: 7.00" wide x 9.25" long x 1.00" tall
Weight: 2.332

This introduction to probability features clear explanations of the mathematics of probability theory and explores its many diverse applications through numerous motivational examples.

Preface
Combinatorial Analysis
Introduction
The Basic Principle of Counting
Permutations
Combinations
Multinomial Coefficients
The Number of Integer Solutions of Equations
Summary
Problems
Theoretical Exercises
Self-Test Problems and Exercises
Axioms of Probability
Introduction
Sample Space and Events
Axioms of Probability
Some Simple Propositions
Sample Spaces Having Equally Likely Outcomes
Probability As a Continuous Set Function
Probability As a Measure of Belief
Summary
Problems
Theoretical Exercises
Self-Test Problems and Exercises
Conditional Probability and Independence
Introduction
Conditional Probabilities
Bayes' Formula
Independent Events
P(-[middle dot]F) is a Probability
Summary
Problems
Theoretical Exercises
Self-Test Problems and Exercises
Random Variables
Random Variables
Discrete Random Variables
Expected Value
Expectatio of a Function of a Random Variable
Variance
The Bernoulli and Binomial Random Variables
Properties of Binomial Random Variables
Computing the Binomial Distribution Function
The Poisson Random Variable
Computing the Poisson Distribution Function
Other Discrete Probability Distribution
The Geometric Random Variable
The Negative Binomial Random Variable
The Hypergeometric Random Variable
The Zeta (or Zipf) distribution
Properties of the Cumulative Distribution Function
Summary
Problems
Theoretical Exercises
Self-Test Problems and Exercises
Continuous Random Variables
Introduction
Expectation and Variance of Continuous Random Variables
The Uniform Random Variable
Normal Random Variables
The Normal Approximation to the Binomial Distribution
Exponential Random Variables
Hazard Rate Functions
Other Continuous Distributions
The Gamma Distribution
The Weibull Distribution
The Cauchy Distribution
The Beta Distribution
The Distribution of a Function of a Random Variable
Summary
Problems
Theoretical Exercises
Self-Test Problems and Exercises
Jointly Distributed Random Variables
Joint Distribution Functions
Independent Random Variables
Sums of Independent Random Variables
Conditional Distributions: Discrete Case
Conditional Distributions: Continuous Case
Order Statistics
Joint Probability Distribution of Functions of Random Variables
Exchangeable Random Variables
Summary
Problems
Theoretical Exercises
Self-Test Problem and Exercises
Properties of Expectation
Introduction
Expectation of Sums of Random Variables
Obtaining Bounds from Expectations via the Probabilistic Method
The Maximum-Minimums Identity
Covariance, Variance of Sums, and Correlations
Conditional Expectation
Definitions
Computing Expectations by Conditioning
Computing Probabilities by Conditioning
Conditional Variance
Conditional Expectation and Prediction
Moment Generating Functions
Joint Moment Generating Functions
Additional Properties of Normal Random Variables
The Multivariate Normal Distribution
The Joint Distribution of the Sample Mean and Sample Variance
General Definition of Expectation
Summary
Problems
Theoretical Exercises
Self-Test Problems and Exercises
Limit Theorems
Introduction
Chebyshev's Inequality and the Weak Law of Large Numbers
The Central Limit Theorem
The Strong Law of Large Numbers
Other Inequalities
Bounding the Error Probability When Approximating a Sum of Independent Bernoulli Random Variables by a Poisson
Summary
Problems
Theoretical Exercises
Self-Test Problems and Exercises
Additional Topics in Probability
The Poisson Process
Markov Chains
Surprise, Uncertainty, and Entropy
Coding Theory and Entropy
Summary
Theoretical Exercises and Problems
Self-Test Problems and Exercises
References
Simulation
Introduction
General Techniques for Simulating Continuous Random Variables
The Inverse Transformation Method
The Rejection Method
Simulating from Discrete Distributions
Variance Reduction Techniques
Use of Antithetic Variables
Variance Reduction by Conditioning
Control Variates
Summary
Problems
Self-Test Problems and Exercises
References
Answers to Selected Problems
Solutions to Self-Test Problems and Exercises
Index

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