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CITATION

Lipschutz, Seymour and Lipson, Marc. Schaum's Outline of Probability, Third Edition. New York: McGraw-Hill Education, 2021.

Schaum's Outline of Probability, Third Edition

Authors: Seymour Lipschutz and Marc Lipson

Published:  November 2021 Pages: 336

eISBN: 9781264258857 | ISBN: 9781264258840
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  • 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