Probability Theory

Probability theory forms the backbone of modern statistics and plays a fundamental role in diverse fields such as economics, engineering, social sciences, medicine, and data science. A sound understanding of its concepts and distributions is therefore essential for students pursuing formal training in statistics. The text begins with the basic foundations of probability, including sample spaces, events, and axiomatic definitions, and gradually progresses to random variables, mathematical expectation, and important discrete and continuous probability distributions. Each topic is supported by worked examples wherever appropriate, and a wide range of exercises designed to strengthen comprehension and encourage independent practice. An effort has been made to use simple language, step-by-step derivations, and consistent notation to make the subject accessible to students encountering probability theory for the first time. At the same time, the book aims to prepare readers for more advanced studies in statistics and related disciplines. The author hopes that this book will serve not only as a textbook for undergraduate students but also as a useful reference for teachers.