Schaum's Outline of Probability, Third Edition

by Seymour Lipschutz, Marc Lipson

Overview

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

Product Details

ISBN-13:	9781264258840
Publisher:	McGraw Hill LLC
Publication date:	11/12/2021
Edition description:	3rd ed.
Pages:	320
Product dimensions:	8.20(w) x 10.80(h) x 1.10(d)

About the Author

Seymour Lipschutz, Ph.D., was on the mathematics faculty of Temple University and previously taught at the Polytechnic Institute of Brooklyn. He was also a visiting professor in the Computer Science Department of Brooklyn College. His work in the Schaum's Outline series includes Beginning Linear Algebra, Discrete Mathematics Fourth Edition, and Linear Algebra, Sixth Edition.

Marc Lipson, Ph.D., is on the faculty of the University of Virginia. Previously, he taught at the University of Georgia, Northeastern University, and Boston University. He is the coauthor of Schaum’s Outline of Discrete Mathematics, Fourth Edition.

Marc Lipson, Ph.D. (Philadelphia, PA), is on the mathematical faculty of the University of Georgia. He is co-author of Schaum's Outline of Discrete Mathematics.

Table of Contents

Chapter 1 Set Theory 1

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 32

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 59

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 85

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 119

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 177

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 224

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 245

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 282

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 309