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# Probability and Statistics for Physical Sciences

- 2nd Edition - September 5, 2023
- Authors: Brian Martin, Mark Hurwitz
- Language: English
- Paperback ISBN:9 7 8 - 0 - 4 4 3 - 1 8 9 6 9 - 2
- eBook ISBN:9 7 8 - 0 - 4 4 3 - 1 8 9 7 0 - 8

Probability and Statistics for Physical Sciences, Second Edition is an accessible guide to commonly used concepts and methods in statistical analysis used in the physical scienc… Read more

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Request a sales quote*Probability and Statistics for Physical Sciences, Second Edition*is an accessible guide to commonly used concepts and methods in statistical analysis used in the physical sciences. This brief yet systematic introduction explains the origin of key techniques, providing mathematical background and useful formulas. The text does not assume any background in statistics and is appropriate for a wide-variety of readers, from first-year undergraduate students to working scientists across many disciplines.

- Provides a collection of useful formulas with mathematical background
- Includes worked examples throughout and end-of-chapter problems for practice
- Offers a logical progression through topics and methods in statistics and probability

- Cover image
- Title page
- Table of Contents
- Copyright
- Preface
- Acknowledgments
- CHAPTER 1. Statistics, experiments, and data
- 1.1 Experiments and observations
- 1.2 Random variables and sampling
- 1.3 Displaying data
- 1.4 Summarizing data numerically
- 1.5 Large samples
- 1.6 Experimental errors
- Problems 1
- CHAPTER 2. Probability
- 2.1. Sample spaces and events
- 2.2. Axioms and calculus of probability
- 2.3. Conditional and marginal probabilities
- 2.4. Permutations and combinations
- 2.5. The meaning of probability
- Problems 2
- CHAPTER 3. Probability distributions I: Basic concepts
- 3.1. Random variables
- 3.2. Single variable
- 3.3. Several variables
- 3.4. Functions of a random variable
- Problems 3
- CHAPTER 4. Probability distributions II: Examples
- 4.1 Continuous variables
- 4.2 Discrete variables
- Problems 4
- CHAPTER 5. Sampling and estimation
- 5.1. Random samples and estimators
- 5.2. Estimators for the mean, variance, and covariance
- 5.3. Laws of large numbers and the central limit theorem
- 5.4. Experimental errors
- 5.5. Monte Carlo method and simulations
- Problems 5
- CHAPTER 6. Sampling distributions associated with the normal distribution
- 6.1. Chi-squared distribution
- 6.2. Student’s t distribution
- 6.3. F distribution
- 6.4. Relations between χ2, t, and F distributions
- Problems 6
- Chapter 7. Parameter estimation I: Maximum likelihood and minimum variance
- 7.1. Estimation of a single parameter
- 7.2. Variance of an estimator
- 7.3. Simultaneous estimation of several parameters
- 7.4. Minimum variance
- Problems 7
- CHAPTER 8. Parameter estimation II: Least-squares and other methods
- 8.1. Unconstrained linear least-squares
- 8.2. Linear least-squares with constraints
- 8.3. Nonlinear least-squares
- 8.4. Other methods
- Problems 8
- CHAPTER 9. Interval estimation
- 9.1 Confidence intervals: Basic ideas
- 9.2 Confidence intervals: General method
- 9.3 Normal distribution
- 9.4 Poisson distribution
- 9.5 Large samples
- 9.6 Confidence intervals near boundaries
- 9.7 Bayesian confidence intervals
- Problems 9
- CHAPTER 10. Hypothesis testing I: Parameters
- 10.1. Statistical hypotheses
- 10.2. General hypotheses: Likelihood ratios
- 10.3. Normal distribution
- 10.4. Other distributions
- 10.5. Analysis of variance
- 10.6. Bayesian hypothesis testing
- Problems 10
- CHAPTER 11. Hypothesis testing II: Other tests
- 11.1 Goodness-of-fit tests
- 11.2 Tests for independence
- 11.3 Nonparametric tests
- Problems 11
- Appendix A. Miscellaneous mathematics
- Appendix B. Optimization of nonlinear functions
- Appendix C. Statistical tables
- Appendix D. Answers to selected problems
- Bibliography
- Index

- No. of pages: 416
- Language: English
- Edition: 2
- Published: September 5, 2023
- Imprint: Academic Press
- Paperback ISBN: 9780443189692
- eBook ISBN: 9780443189708

BM

### Brian Martin

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### Mark Hurwitz

Dr. Mark F. Hurwitz** **graduated from Northwestern University with a BS in Mechanical Engineering and then worked as an engineer at Xerox Corporation while earning an MS in Mechanical and Aerospace Engineering at the University of Rochester. He earned a PhD at Cornell University in Theoretical and Applied Mechanics during an extensive R&D career in the filtration and separations industry at Pall Corporation, where he was inventor of 12 US patents with multiple foreign cognates. Returning to Cornell University, he was an Adjunct Professor in the Robert Frederick Smith School of Chemical and Biomolecular Engineering, before moving to administration and becoming the Chief Research Compliance Officer.

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