Theory of Probability and Statistics

Dr. Humbat Aliyev is an Associate Professor of Mathematics and has served both as a full-time faculty member and as a visiting professor and researcher at universities in several countries, including the Russian Federation and Kazakhstan. He has served as a visiting professor in various countries, including Malaysia and Turkey. For the past 35 years, Dr. Aliyev has been actively engaged in both research and teaching. His primary research areas include mechanics, differential equations, and probability theory. He is widely regarded as a distinguished scholar, dedicated educator, and productive researcher. Over his 30-year career in education, he authored more than ten books across a range of subjects. Dr. Aliyev is a pioneering scientist and distinguished educator who has had a profound impact through his long-standing service, steadfast commitment, and tireless dedication. Dr. Rakib F. Efendiev is a Professor of Mathematics at Baku Engineering University with a PhD in Mathematical Analysis and Doctor of Science in Differential Equations. His research spans spectral theory, inverse problems, differential operators, and applied mathematical modeling, with publications in internationally indexed journals such as Boundary Value Problems and Partial Differential Equations in Applied Mathematics. He has participated in and organized numerous international conferences and has served as a reviewer for Mathematical Reviews and Zentralblatt MATH. Alongside his research activity, Dr. Efendiev has over three decades of teaching experience, delivering core courses in probability, statistics, calculus, and differential equations. His pedagogical focus emphasizes clarity, rigor, and problem-based learning, which directly informs the structure and methodology of this book. Dr. Praveen Agarwal earned his Ph. D. in Mathematics at the Malviya National Institute of Technology (MNIT) in Jaipur, India, in 2006. Recently, Prof. Agarwal has been listed as the World's Top 2% Scientist from 2020-2025, released by Stanford University. In the 2025 ranking of best scientists worldwide announced by Research.com, he ranked 13th at the India level and 1297th worldwide in Mathematics. Dr. Agarwal has been actively involved in research as well as pedagogical activities for the last 24 years. His major research interests include Special Functions, Fractional Calculus, Numerical Analysis, Differential and Difference Equations, Inequalities, Probability & Statistics, and Fixed Point Theorems. He has published 11 research monographs and edited volumes and more than 405 publications (with almost 100 mathematicians all over the world) in prestigious national and international mathematics journals. Dr. Agarwal worked previously either as a regular faculty or as a visiting professor and scientist in universities in several countries, including India, Germany, Turkey, South Korea, UK, Russia, Malaysia and Thailand. He has served over 50 Journals in the capacity of an Editor/Honorary Editor, or Associate Editor, and published 15 books as an editor.

• 1. Organization and description of data2. Probability3. Discrete random variables and probability distributions4. Continuous random variables and their probability distributions5. Sampling distributions6. Interval estimation7. Hypothesis testing8. Some nonparametric tests9. Simple linear regression Appendix and References