This course is an introduction to the probability tools and concepts that will be necessary for the theory of hypothesis testing. We will cover the first five chapters of the book. That is, we will learn about the distribution of vandom variables and random vectors (discrete and continuous), the special distributions related to statistics, distribution of the functions of random variables, moment generating functions, and lastly, limiting distributions and the central limit theorem. The rest of the chapters will be covered in math 555. We will have four exams each worth 25\% of your grade. In order to pass the course, you need to obtain an average of 50\% or more.