This chapter introduces some important discrete and continuous random variable distributions, presents the relations between some of these random variables, depicts the concepts of functions of random variables, and discusses the Taylor series, a powerful tool for approximating analytic functions. Certain types of random variables occur over and over again in applications. The hypergeometric distribution arises in probabilistic experiments in which objects are divided into two distinct classes (class 1 and class 2). The normal or Gaussian distribution function is ubiquitous throughout the world of statistics and probability. Exponential random variables are widely adopted in performance and reliability modeling. The Taylor-Maclaurin series are potent tools for approximating analytic functions that can be difficult to calculate.