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Lipschutz, Seymour and Lipson, Marc Lars. Schaum's Outline of Theory and Problems of Probability, Second Edition. US: McGraw-Hill Education, 2000.

Schaum's Outline of Theory and Problems of Probability, Second Edition

Authors: Seymour Lipschutz and Marc Lars Lipson

Published:  2000

ISBN: 9780071386517 0071352031
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  • 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 Binomial and Normal Distributions
  • 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 Processes
  • 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.4 Measures of Dispersion: Variance and Standard Deviation.
  • A.3 Measures of Central Tendency; Mean and Median.
  • 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