This book provides a step to enter into the knowledge base of Probability and distribution theory. The graduation and post-graduation level students will get a benefit from the book as it contains a huge number of elaborations of different theorems and different types of applications to the respective theories. The mean and variances of different continuous and discrete random variables are shown in very lucid manner. The book is also enriched with different harder sums collected from different University examinations which will provide a large area to exercise of brain for the beginners. Introduction of each chapter contains motivational points, real life examples and theoretical demonstrations which will develop the interest of the student about probability and distribution theory. This book will not only gives a platform for the students for self-practicing but also it will provide an arena to build up base knowledge in probability and distribution theory.