Study smarter and stay on top of your probability course with the bestselling Schaum’s Outline―now with the NEW Schaum's app and website!
Schaum’s Outline of Probability, Third Edition is the go-to study guide for help in probability courses. It's ideal for undergrads, graduate students and professionals needing a tool for review. With an outline format that facilitates quick and easy review and mirrors the course in scope and sequence, this book helps you understand basic concepts and get the extra practice you need to excel in the course. Schaum's Outline of Probability, Third Edition supports the bestselling textbooks and is useful for a variety of classes, including Elementary Probability and Statistics, Data Analysis, Finite Mathematics, and many other courses.
You’ll find coverage on finite and countable sets, binomial coefficients, axioms of probability, conditional probability, expectation of a finite random variable, Poisson distribution, and probability of vectors and Stochastic matrices. Also included: finite Stochastic and tree diagrams, Chebyshev’s inequality and the law of large numbers, calculations of binomial probabilities using normal approximation, and regular Markov processes and stationary state distributions.
Features
• NEW to this edition: the new Schaum's app and website!
• NEW to this edition: 25 NEW problem-solving videos online
• 430 solved problems
• Outline format to provide a concise guide to the standard college course in probability
• Clear, concise explanations of probability concepts
• Supports these major texts: Elementary Statistics: A Step by Step Approach (Bluman), Mathematics with Applications (Hungerford), and Discrete Mathematics and Its Applications (Rosen)
• Appropriate for the following courses: Elementary Probability and Statistics, Data Analysis, Finite Mathematics, Introduction to Mathematical Statistics, Mathematics for Biological Sciences, Introductory Statistics, Discrete Mathematics, Probability for Applied Science, and Introduction to Probability Theory
Author(s): Seymour Lipschutz, Marc Lipson
Series: Schaum's Outlines
Edition: 3
Publisher: McGraw-Hill Education
Year: 2021
Language: English
Commentary: Vector PDF
Pages: 320
City: New York, NY
Tags: Bayesian Inference; Probability Theory; Set Theory; Markov Chains
Cover
Title Page
Copyright Page
Preface
Contents
CHAPTER 1 Set Theory
1.1 Introduction
1.2 Sets and Elements, Subsets
1.3 Venn Diagrams
1.4 Set Operations
1.5 Finite and Countable Sets
1.6 Counting Elements in Finite Sets, Inclusion-Exclusion Principle
1.7 Products Sets
1.8 Classes of Sets, Power Sets, Partitions
1.9 Mathematical Induction
CHAPTER 2 Techniques of Counting
2.1 Introduction
2.2 Basic Counting Principles
2.3 Factorial Notation
2.4 Binomial Coefficients
2.5 Permutations
2.6 Combinations
2.7 Tree Diagrams
CHAPTER 3 Introduction to Probability
3.1 Introduction
3.2 Sample Space and Events
3.3 Axioms of Probability
3.4 Finite Probability Spaces
3.5 Infinite Sample Spaces
3.6 Classical Birthday Problem
CHAPTER 4 Conditional Probability and Independence
4.1 Introduction
4.2 Conditional Probability
4.3 Finite Stochastic and Tree Diagrams
4.4 Partitions, Total Probability, and Bayes’ Formula
4.5 Independent Events
4.6 Independent Repeated Trials
CHAPTER 5 Random Variables
5.1 Introduction
5.2 Random Variables
5.3 Probability Distribution of a Finite Random Variable
5.4 Expectation of a Finite Random Variable
5.5 Variance and Standard Deviation
5.6 Joint Distribution of Random Variables
5.7 Independent Random Variables
5.8 Functions of a Random Variable
5.9 Discrete Random Variables in General
5.10 Continuous Random Variables
5.11 Cumulative Distribution Function
5.12 Chebyshev’s Inequality and the Law of Large Numbers
CHAPTER 6 Random Variable Models
6.1 Introduction
6.2 Bernoulli Trials, Binomial Distribution
6.3 Normal Distribution
6.4 Evaluating Normal Probabilities
6.5 Normal Approximation of the Binomial Distribution
6.6 Calculations of Binomial Probabilities Using the Normal Approximation
6.7 Poisson Distribution
6.8 Miscellaneous Discrete Random Variables
6.9 Miscellaneous Continuous Random Variables
CHAPTER 7 Markov Chains
7.1 Introduction
7.2 Vectors and Matrices
7.3 Probability Vectors and Stochastic Matrices
7.4 Transition Matrix of a Markov Process
7.5 State Distributions
7.6 Regular Markov Processes and Stationary State Distributions
APPENDIX A Descriptive Statistics
A.1 Introduction
A.2 Frequency Tables, Histograms
A.3 Measures of Central Tendency; Mean and Median,
A.4 Measures of Dispersion: Variance and Standard Deviation
A.5 Bivariate Data, Scatterplots, Correlation Coefficients
A.6 Methods of Least Squares, Regression Line, Curve Fitting.
APPENDIX B Chi-Square Distribution
B.1 Introduction
B.2 Goodness of Fit, Null Hypothesis, Critical Values
B.3 Goodness of Fit for Uniform and Prior Distributions
B.4 Goodness of Fit for Binomial Distribution
B.5 Goodness of Fit for Normal Distribution
B.6 Chi-Square Test for Independence
B.7 Chi-Square Test for Homogeneity
Index
