Introduction to probability statistics & R: foundations for data-based sciences/ Sujit K Sahu

Includes bibliography and index

Part I: Introduction to basic statistics and R --
1. Introduction to basic statistics -- 2. Getting started with R --
Part II: Introduction to probability --
3. Introduction to probability -- 4. Conditional probability and independence -- 5. Random variables and their probability distributions -- 6. Standard discrete distributions -- 7. Standard continuous distributions -- 8. Joint distributions and the CLT --
Part III: Introduction to statistical inference --
9. Introduction to statistical inference -- 10. Methods of point estimation -- 11. Interval estimation -- 12. Hypothesis testing --
Part IV: Advanced distribution theory and probability --
13. Generating functions -- 14. Transformation and transformed distributions -- 15. Multivariate distributions -- Convergence estimators -- Part V Introduction to statistical modelling --
17. Simple linear regression model -- 18. Multiple Linear regression model -- 19. Analysis of variance -- 20. Solutions to selected exercises -- A Appendix: Table of common probability distributions

The book comprises 19 chapters divided into five parts. Part I introduces basic statistics and the R software package, teaching readers to calculate simple statistics and create basic data graphs. Part II delves into probability concepts, including rules and conditional probability, and introduces widelyused discrete and continuous probability distributions (e.g., binomial, Poisson, normal, log-normal). It concludes with the central limit theorem and joint distributions for multiple random variables. Part III explores statistical inference,
covering point and interval estimation, hypothesis testing, and Bayesian inference. This part is intentionally less technical, making it accessible to readers without an extensive mathematical background. Part IV addresses advanced probability and statistical distribution theory, assuming some familiarity with (or concurrent study of) mathematical methods like advanced calculus and linear algebra. Finally, Part V focuses on advanced statistical modelling using simple and multiple regression and analysis of variance, laying the foundation for further studies in machine learning and data science applicable to various data and decision analytics contexts.

Based on years of teaching experience, this textbook includes numerousexercises and makes extensive use of R, making it ideal for year-long data science modules and courses. In addition to university courses, the book amply covers the syllabus for the Actuarial Statistics 1 examination of the Institute and Faculty of Actuaries in London. It also provides a solid foundation for postgraduate studies in statistics and probability, or a reliable reference for statistics.