Probability With Applications and R 2nd Edition by Amy S Wagaman ,Robert P Dobrow ISBN 1119692385 978-1119692386

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ISBN 10:1119692385

ISBN 13:978-1119692386 

Author:Amy S.Wagaman ,Robert P.Dobrow

Discover the latest edition of a practical introduction to the theory of probability, complete with R code samples

In the newly revised Second Edition of Probability: With Applications and R, distinguished researchers Drs. Robert Dobrow and Amy Wagaman deliver a thorough introduction to the foundations of probability theory. The book includes a host of chapter exercises, examples in R with included code, and well-explained solutions. With new and improved discussions on reproducibility for random numbers and how to set seeds in R, and organizational changes, the new edition will be of use to anyone taking their first probability course within a mathematics, statistics, engineering, or data science program.

New exercises and supplemental materials support more engagement with R, and include new code samples to accompany examples in a variety of chapters and sections that didn’t include them in the first edition.

The new edition also includes for the first time: 

• A thorough discussion of reproducibility in the context of generating random numbers
• Revised sections and exercises on conditioning, and a renewed description of specifying PMFs and PDFs
• Substantial organizational changes to improve the flow of the material
• Additional descriptions and supplemental examples to the bivariate sections to assist students with a limited understanding of calculus

Perfect for upper-level undergraduate students in a first course on probability theory, Probability: With Applications and R is also ideal for researchers seeking to learn probability from the ground up or those self-studying probability for the purpose of taking advanced coursework or preparing for actuarial exams.

Table of contents: 

First Principles

• Random Experiment, Sample Space, Event

• What Is a Probability?

• Probability Function

• Properties of Probabilities

• Equally Likely Outcomes

• Counting I

        Permutations

• Counting II

• Combinations and Binomial Coefficients

• Problem-Solving Strategies: Complements and Inclusion–Exclusion

• A First Look at Simulation

• Summary

• Exercises

Conditional Probability and Independence

• Conditional Probability

• New Information Changes the Sample Space

• Finding P (A and B)

• Birthday Problem

• Conditioning and the Law of Total Probability

• Bayes Formula and Inverting a Conditional Probability

• Independence and Dependence

• Product Spaces

• Summary

• Exercises

Introduction to Discrete Random Variables

• Random Variables

• Independent Random Variables

• Bernoulli Sequences

• Binomial Distribution

• Poisson Distribution

• Poisson Approximation of Binomial Distribution

• Poisson as Limit of Binomial Probabilities

• Summary

• Exercises

Expectation and More with Discrete Random Variables

• Expectation

• Functions of Random Variables

• Joint Distributions

• Independent Random Variables

• Sums of Independent Random Variables

• Linearity of Expectation

• Variance and Standard Deviation

• Covariance and Correlation

• Conditional Distribution

• Introduction to Conditional Expectation

• Properties of Covariance and Correlation

• Expectation of a Function of a Random Variable

• Summary

• Exercises

More Discrete Distributions and Their Relationships

• Geometric Distribution

• Memorylessness

• Coupon Collecting and Tiger Counting

• Moment-Generating Functions

• Negative Binomial—Up from the Geometric

• Hypergeometric—Sampling Without Replacement

• From Binomial to Multinomial

• Benford’s Law

• Summary

• Exercises

Continuous Probability

• Probability Density Function

• Cumulative Distribution Function

• Expectation and Variance

• Uniform Distribution

• Exponential Distribution

• Memorylessness

• Joint Distributions

• Independence

• Accept–Reject Method

• Covariance, Correlation

• Summary

• Exercises

Continuous Distributions

• Normal Distribution

• Standard Normal Distribution

• Normal Approximation of Binomial Distribution

• Quantiles

• Sums of Independent Normals

• Gamma Distribution

• Probability as a Technique of Integration

• Poisson Process

• Beta Distribution

• Pareto Distribution

• Summary

• Exercises

Densities of Functions of Random Variables

• Densities via CDFs

• Simulating a Continuous Random Variable

• Method of Transformations

• Maximums, Minimums, and Order Statistics

• Convolution

• Geometric Probability

• Transformations of Two Random Variables

• Summary

• Exercises

Conditional Distribution, Expectation, and Variance

• Introduction

• Conditional Distributions

• Discrete and Continuous: Mixing it Up

• Conditional Expectation

• From Function to Random Variable

• Random Sum of Random Variables

• Computing Probabilities by Conditioning

• Conditional Variance

• Bivariate Normal Distribution

• Summary

• Exercises

Limits

• Weak Law of Large Numbers

  • Markov and Chebyshev Inequalities

• Strong Law of Large Numbers

• Method of Moments

• Monte Carlo Integration

• Central Limit Theorem

• Central Limit Theorem and Monte Carlo

• A Proof of the Central Limit Theorem

• Summary

• Exercises

Beyond Random Walks and Markov Chains

• Random Walk on Graphs

• Long-Term Behavior

• Random Walks on Weighted Graphs and Markov Chains

• Stationary Distribution

• From Markov Chain to Markov Chain Monte Carlo

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Tags: Amy S Wagaman, Robert P Dobrow, Probability, Applications